Universality in nonequilibrium lattice systems: theoretical foundations
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Hackensack, NJ [u.a.]
World Scientific
2008
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIX, 276 S. Ill., graph. Darst. 24 cm |
| ISBN: | 981281227X 9789812812278 |
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| 100 | 1 | |a Ódor, Géza |d 1960- |e Verfasser |0 (DE-588)136693814 |4 aut | |
| 245 | 1 | 0 | |a Universality in nonequilibrium lattice systems |b theoretical foundations |c Géza Ódor |
| 264 | 1 | |a Hackensack, NJ [u.a.] |b World Scientific |c 2008 | |
| 300 | |a XIX, 276 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Scaling laws (Statistical physics) | |
| 650 | 4 | |a Lattice theory | |
| 650 | 4 | |a Self-organizing systems | |
| 650 | 4 | |a Phase transformations (Statistical physics) | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Lattice theory | |
| 650 | 4 | |a Phase transformations (Statistical physics) | |
| 650 | 4 | |a Scaling laws (Statistical physics) | |
| 650 | 4 | |a Self-organizing systems | |
| 650 | 0 | 7 | |a Gittermodell |0 (DE-588)4226961-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Universalität |0 (DE-588)4186918-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtgleichgewicht |0 (DE-588)4171730-2 |2 gnd |9 rswk-swf |
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| adam_text | Contents
Preface
v
Acknowledgments
xiii
1.
Introduction
1
1.1
Critical exponents of equilibrium (thermal) systems
... 1
1.2
Static percolation cluster exponents
............ 2
1.3
Dynamical critical exponents
................ 4
1.4
Crossover between classes
.................. 9
1.5
Critical exponents and relations of spreading processes
. . 10
1.5.1
Damage spreading exponents
............ 12
1.6
Field theoretical approach to reaction-diffusion systems
. 13
1.6.1
Classification scheme of one-component, bosonic
RD models, with short ranged interactions and
memory
........................ 17
1.6.2
Ageing and local scale
invariance
(LSI)
...... 20
1.7
The effect of disorder
..................... 23
2.
Out of Equilibrium Classes
27
2.1
Field theoretical description of dynamical classes at and
below Tc
............................ 27
2.2
Dynamical classes at Tc
> 0................. 30
2.3
Ising classes
.......................... 31
2.3.1
Correlated percolation clusters at Tc
....... 32
2.3.2
Dynamical Ising classes
............... 33
2.3.3
Competing dynamics added to spin-flip
...... 37
2.3.4
Competing dynamics added to spin-exchange
... 40
xvi
Universality in Nonequilibrium Lattice Systems
2.3.5
Long-range interactions and correlations
..... 40
2.3.6
Damage spreading behavior
............ 41
2.3.7
Disordered Ising classes
............... 41
2.4
Potts classes
.......................... 45
2.4.1
Correlated percolation at Tc
............ 46
2.4.2
The vector Potts (clock) model
........... 47
2.4.3
Dynamical Potts classes
............... 47
2.4.4
Long-range interactions
............... 49
2.5
XY model classes
....................... 49
2.5.1
Long-range correlations
............... 51
2.6
O(N) symmetric model classes
............... 52
2.6.1
Correlated percolation at Tc
............ 53
2.6.2
Disordered O(N) classes
.............. 54
3.
Genuine Basic Nonequilibrium Classes with Fluctuating
Ordered States
55
3.1
Driven lattice gas (DLG) classes
.............. 55
3.1.1
Driven lattice gas model in two-dimensional
(DDS)
........................ 56
3.1.2
Driven lattice gas model in one-dimensional
(ASEP, ZRP)
.................... 57
3.1.3
Driven lattice gas with disorder
.......... 62
3.1.4
Critical behavior of self-propelled particles
.... 63
4.
Genuine Basic Nonequilibrium Classes with Absorbing State
65
4.1
Mean-field classes of general
пА
—>
(η
+
к) А,
πιΑ
—>
(m
—
I)A processes
.................. 67
4.1.1
Bosonic
models
................... 68
4.1.2
Site restricted (fermionic) models
......... 68
4.1.3
The
η
=
m
symmetric case
............. 69
4.1.4
The
η
>
m
asymmetric case
............ 70
4.1.5
The asymmetric
η
<
m
case
............ 71
4.1.6
Upper critical behavior and below
......... 72
4.2
Directed percolation (DP) classes
.............. 73
4.2.1
The contact process
................. 81
4.2.2
Two-point correlations, ageing properties
..... 82
4.2.3
DP-class stochastic cellular automata
....... 83
4.2.4
Branching and annihilating random walks with
odd number of offspring
............... 87
Contents xvii
4.2.5 DP
with spatial boundary conditions
....... 87
4.2.6
DP with mixed (parabolic) boundary conditions
. 91
4.2.7
Levy flight anomalous diffusion in DP
....... 91
4.2.8
Long-range correlated initial conditions in DP
. . 93
4.2.9 Anisotropie DP
systems
............... 95
4.2.10
Quench disordered DP classes
........... 95
4.3
Generalized, n-particle contact processes
.......... 99
4.4
Dynamical
isotropie
percolation (DIP) classes
....... 103
4.4.1
Static
isotropie
percolation universality classes
. . 104
4.4.2
DIP with spatial boundary conditions
....... 106
4.4.3
Levy flight anomalous diffusion in DIP
...... 106
4.5
Voter model (VM) classes
.................. 107
4.5.1
The
2Л
-> 0
(ARW) and the 2A
->
A models
... 109
4.5.2
Compact DP (CDP) with spatial boundary
conditions
......................
Ill
4.5.3
CDP with parabolic boundary conditions
.....
HI
4.5.4
Levy flight anomalous diffusion in ARW-s
..... 112
4.5.5
ARW with anisotropy
................ 114
4.5.6
ARW with quenched disorder
........... 115
4.6
Parity conserving (PC) classes
............... 116
4.6.1
Branching and annihilating random walks with
even number of offspring (BARWe)
........ 117
4.6.2
The
NEKIM
model
................. 122
4.6.3
Parity conserving, stochastic cellular automata
. . 127
4.6.4
PC class surface catalytic models
......... 129
4.6.5
Long-range correlated initial conditions
...... 132
4.6.6
Spatial boundary conditions
............ 133
4.6.7
BARWe with long-range interactions
....... 136
4.6.8
Parity conserving NEKIMCA with quenched
disorder
........................ 137
4.6.9 Anisotropie PC
systems
............... 140
4.7
Classes in models with
η
<
m
production and
m
particle
annihilation at ac
= 0.................... 143
4.8
Classes in models with
η
<
m
production and
m
particle
coagulation at ac
= 0;
reversible reactions
(IR)
...... 146
4.9
Generalized PC models
................... 150
4.10
Multiplicative noise classes
................. 152
5.
Scaling at First-Order Phase Transitions
155
xviii
Universality in Nonequilibrium Lattice Systems
5.1
Tricritical directed percolation classes (TDP)
....... 159
5.2
Tricritical DIP classes
.................... 163
6.
Universality Classes of Multi-Component Systems
165
6.1
The A
+
В
-> 0
classes
.................... 165
6.1.1
Reversible A + A^C and A + B^C class
. . 167
6.1.2 Anisotropie
A
+
В
-> 0............... 168
6.1.3
Disordered A
+
В
-> 0
models
........... 169
6.2
A A
-» 0,
B5
-> 0
with hard-core exclusion
........ 169
6.3
Symmetrical, multi-species
A¡
+
A,·
-+ 0
(q-MAM)
classes
............................. 171
6.4
Heterogeneous, multi-species
Aj + Aj
—> 0
system
..... 173
6.5
Unidirectionally coupled ARW classes
........... 175
6.6
DP coupled to frozen field classes
.............. 176
6.6.1
The pair contact process
(PCP)
model
...... 178
6.6.2
The threshold transfer process (TTP)
....... 180
6.7
DP with coupled diffusive field classes
........... 182
6.7.1
The PCPD model
.................. 184
6.7.2
Cyclically coupled spreading with pair
annihilation
..................... 188
6.7.3
The parity conserving annihilation-fission model
. 188
6.7.4
The driven PCPD model
.............. 189
6.8
BARWe with coupled non-diffusive field class
....... 190
6.9
DP with diffusive, conserved slave field classes
....... 190
6.10
DP with frozen, conserved slave field classes
........ 193
6.10.1
Realizations of NDCF classes,
SOC
models
.... 195
6.10.2
NDCF with anisotropy
............... 199
6.10.3
NDCF with spatial boundary conditions
..... 199
6.11
Coupled iV-component DP classes
............. 200
6.12
Coupled TV-component BARW2 classes
........... 200
6.12.1
Generalized contact processes with
η
> 2
absorbing states in one dimension
......... 202
6.13
Hard-core 2-BARW2 classes in one dimension
....... 203
6.13.1
Hard-core 2-BARWo models in one dimension
. . 204
6.13.2
Coupled binary spreading processes
........ 205
7.
Surface-Interface Growth Classes
209
7.1
The random deposition class
................ 212
Contents xix
7.2 Edwards-
Wilkinson (EW) classes
.............. 213
7.3
Quench disordered EW classes (QEW)
........... 213
7.3.1
EW classes with boundaries
............ 214
7.4
Kardar-Parisi-Zhang (KPZ) classes
............. 216
7.4.1
KPZ with anisotropy
................ 218
7.4.2
The Kuramoto-Sivashinsky (KS) Equation
.... 219
7.4.3
Quench disordered KPZ (QKPZ) classes
..... 220
7.4.4
KPZ classes with boundaries
............ 221
7.5
Other continuum growth classes
............... 223
7.5.1
Molecular beam epitaxy classes (MBE)
...... 223
7.5.2
The Bradley-Harper (BH) model
.......... 225
7.5.3
Classes of mass adsorption-desorption aggregation
and chipping models
(SOC)
............ 225
7.6
Unidirectionally coupled DP classes
............ 229
7.6.1
Monomer adsorption-desorption at terraces
.... 230
7.7
Unidirectionally coupled PC classes
............. 232
7.7.1
Dimer adsorption-desorption at terraces
...... 233
8.
Summary and Outlook
239
Appendix
245
Bibliography
249
Universality in
Nonequilìbrium
Lattice Systems
Theoretical Foundations
in terms of their collective behavior due to a diverging correlation
length. This book provides a comprehensive overview of
dynamical universality classes occurring in nonequilibrium
systems defined on regular lattices. The factors determining these
diverse universality classes have yet to be fully understood, but
the book attempts to summarize our present knowledge, taking
them into account systematically.
The book helps the reader to navigate in the zoo of basic models
and classes that were investigated in the past decades, using field
theoretical formalism and topological diagrams of phase spaces.
Based on a review in Rev. Mod. Phys. by the author, it incorporates
surface growth classes, classes of spin models, percolation and
multi-component system classes as well as damage spreading
transitions. (The success of that review can be quantified by the
more than one hundred independent citations of that paper since
2004.)
The extensions in this book include new topics like local scale
invariance,
uncritical points, phase space topologies, nonperturbative
renormalization group results and disordered systems that are
discussed in more detail. This book also aims to be more
pedagogical, providing more background and derivation of results.
Topological phase space diagrams introduced by Kamenev
(Physical
Reviť» E
2006)
very recentlv are used as a guide for
one-component, reaction-diffusion sv stems.
|
| adam_txt |
Contents
Preface
v
Acknowledgments
xiii
1.
Introduction
1
1.1
Critical exponents of equilibrium (thermal) systems
. 1
1.2
Static percolation cluster exponents
. 2
1.3
Dynamical critical exponents
. 4
1.4
Crossover between classes
. 9
1.5
Critical exponents and relations of spreading processes
. . 10
1.5.1
Damage spreading exponents
. 12
1.6
Field theoretical approach to reaction-diffusion systems
. 13
1.6.1
Classification scheme of one-component, bosonic
RD models, with short ranged interactions and
memory
. 17
1.6.2
Ageing and local scale
invariance
(LSI)
. 20
1.7
The effect of disorder
. 23
2.
Out of Equilibrium Classes
27
2.1
Field theoretical description of dynamical classes at and
below Tc
. 27
2.2
Dynamical classes at Tc
> 0. 30
2.3
Ising classes
. 31
2.3.1
Correlated percolation clusters at Tc
. 32
2.3.2
Dynamical Ising classes
. 33
2.3.3
Competing dynamics added to spin-flip
. 37
2.3.4
Competing dynamics added to spin-exchange
. 40
xvi
Universality in Nonequilibrium Lattice Systems
2.3.5
Long-range interactions and correlations
. 40
2.3.6
Damage spreading behavior
. 41
2.3.7
Disordered Ising classes
. 41
2.4
Potts classes
. 45
2.4.1
Correlated percolation at Tc
. 46
2.4.2
The vector Potts (clock) model
. 47
2.4.3
Dynamical Potts classes
. 47
2.4.4
Long-range interactions
. 49
2.5
XY model classes
. 49
2.5.1
Long-range correlations
. 51
2.6
O(N) symmetric model classes
. 52
2.6.1
Correlated percolation at Tc
. 53
2.6.2
Disordered O(N) classes
. 54
3.
Genuine Basic Nonequilibrium Classes with Fluctuating
Ordered States
55
3.1
Driven lattice gas (DLG) classes
. 55
3.1.1
Driven lattice gas model in two-dimensional
(DDS)
. 56
3.1.2
Driven lattice gas model in one-dimensional
(ASEP, ZRP)
. 57
3.1.3
Driven lattice gas with disorder
. 62
3.1.4
Critical behavior of self-propelled particles
. 63
4.
Genuine Basic Nonequilibrium Classes with Absorbing State
65
4.1
Mean-field classes of general
пА
—>
(η
+
к) А,
πιΑ
—>
(m
—
I)A processes
. 67
4.1.1
Bosonic
models
. 68
4.1.2
Site restricted (fermionic) models
. 68
4.1.3
The
η
=
m
symmetric case
. 69
4.1.4
The
η
>
m
asymmetric case
. 70
4.1.5
The asymmetric
η
<
m
case
. 71
4.1.6
Upper critical behavior and below
. 72
4.2
Directed percolation (DP) classes
. 73
4.2.1
The contact process
. 81
4.2.2
Two-point correlations, ageing properties
. 82
4.2.3
DP-class stochastic cellular automata
. 83
4.2.4
Branching and annihilating random walks with
odd number of offspring
. 87
Contents xvii
4.2.5 DP
with spatial boundary conditions
. 87
4.2.6
DP with mixed (parabolic) boundary conditions
. 91
4.2.7
Levy flight anomalous diffusion in DP
. 91
4.2.8
Long-range correlated initial conditions in DP
. . 93
4.2.9 Anisotropie DP
systems
. 95
4.2.10
Quench disordered DP classes
. 95
4.3
Generalized, n-particle contact processes
. 99
4.4
Dynamical
isotropie
percolation (DIP) classes
. 103
4.4.1
Static
isotropie
percolation universality classes
. . 104
4.4.2
DIP with spatial boundary conditions
. 106
4.4.3
Levy flight anomalous diffusion in DIP
. 106
4.5
Voter model (VM) classes
. 107
4.5.1
The
2Л
-> 0
(ARW) and the 2A
->
A models
. 109
4.5.2
Compact DP (CDP) with spatial boundary
conditions
.
Ill
4.5.3
CDP with parabolic boundary conditions
.
HI
4.5.4
Levy flight anomalous diffusion in ARW-s
. 112
4.5.5
ARW with anisotropy
. 114
4.5.6
ARW with quenched disorder
. 115
4.6
Parity conserving (PC) classes
. 116
4.6.1
Branching and annihilating random walks with
even number of offspring (BARWe)
. 117
4.6.2
The
NEKIM
model
. 122
4.6.3
Parity conserving, stochastic cellular automata
. . 127
4.6.4
PC class surface catalytic models
. 129
4.6.5
Long-range correlated initial conditions
. 132
4.6.6
Spatial boundary conditions
. 133
4.6.7
BARWe with long-range interactions
. 136
4.6.8
Parity conserving NEKIMCA with quenched
disorder
. 137
4.6.9 Anisotropie PC
systems
. 140
4.7
Classes in models with
η
<
m
production and
m
particle
annihilation at ac
= 0. 143
4.8
Classes in models with
η
<
m
production and
m
particle
coagulation at ac
= 0;
reversible reactions
(IR)
. 146
4.9
Generalized PC models
. 150
4.10
Multiplicative noise classes
. 152
5.
Scaling at First-Order Phase Transitions
155
xviii
Universality in Nonequilibrium Lattice Systems
5.1
Tricritical directed percolation classes (TDP)
. 159
5.2
Tricritical DIP classes
. 163
6.
Universality Classes of Multi-Component Systems
165
6.1
The A
+
В
-> 0
classes
. 165
6.1.1
Reversible A + A^C and A + B^C class
. . 167
6.1.2 Anisotropie
A
+
В
-> 0. 168
6.1.3
Disordered A
+
В
-> 0
models
. 169
6.2
A A
-» 0,
B5
-> 0
with hard-core exclusion
. 169
6.3
Symmetrical, multi-species
A¡
+
A,·
-+ 0
(q-MAM)
classes
. 171
6.4
Heterogeneous, multi-species
Aj + Aj
—> 0
system
. 173
6.5
Unidirectionally coupled ARW classes
. 175
6.6
DP coupled to frozen field classes
. 176
6.6.1
The pair contact process
(PCP)
model
. 178
6.6.2
The threshold transfer process (TTP)
. 180
6.7
DP with coupled diffusive field classes
. 182
6.7.1
The PCPD model
. 184
6.7.2
Cyclically coupled spreading with pair
annihilation
. 188
6.7.3
The parity conserving annihilation-fission model
. 188
6.7.4
The driven PCPD model
. 189
6.8
BARWe with coupled non-diffusive field class
. 190
6.9
DP with diffusive, conserved slave field classes
. 190
6.10
DP with frozen, conserved slave field classes
. 193
6.10.1
Realizations of NDCF classes,
SOC
models
. 195
6.10.2
NDCF with anisotropy
. 199
6.10.3
NDCF with spatial boundary conditions
. 199
6.11
Coupled iV-component DP classes
. 200
6.12
Coupled TV-component BARW2 classes
. 200
6.12.1
Generalized contact processes with
η
> 2
absorbing states in one dimension
. 202
6.13
Hard-core 2-BARW2 classes in one dimension
. 203
6.13.1
Hard-core 2-BARWo models in one dimension
. . 204
6.13.2
Coupled binary spreading processes
. 205
7.
Surface-Interface Growth Classes
209
7.1
The random deposition class
. 212
Contents xix
7.2 Edwards-
Wilkinson (EW) classes
. 213
7.3
Quench disordered EW classes (QEW)
. 213
7.3.1
EW classes with boundaries
. 214
7.4
Kardar-Parisi-Zhang (KPZ) classes
. 216
7.4.1
KPZ with anisotropy
. 218
7.4.2
The Kuramoto-Sivashinsky (KS) Equation
. 219
7.4.3
Quench disordered KPZ (QKPZ) classes
. 220
7.4.4
KPZ classes with boundaries
. 221
7.5
Other continuum growth classes
. 223
7.5.1
Molecular beam epitaxy classes (MBE)
. 223
7.5.2
The Bradley-Harper (BH) model
. 225
7.5.3
Classes of mass adsorption-desorption aggregation
and chipping models
(SOC)
. 225
7.6
Unidirectionally coupled DP classes
. 229
7.6.1
Monomer adsorption-desorption at terraces
. 230
7.7
Unidirectionally coupled PC classes
. 232
7.7.1
Dimer adsorption-desorption at terraces
. 233
8.
Summary and Outlook
239
Appendix
245
Bibliography
249
Universality in
Nonequilìbrium
Lattice Systems
Theoretical Foundations
in terms of their collective behavior due to a diverging correlation
length. This book provides a comprehensive overview of
dynamical universality classes occurring in nonequilibrium
systems defined on regular lattices. The factors determining these
diverse universality classes have yet to be fully understood, but
the book attempts to summarize our present knowledge, taking
them into account systematically.
The book helps the reader to navigate in the zoo of basic models
and classes that were investigated in the past decades, using field
theoretical formalism and topological diagrams of phase spaces.
Based on a review in Rev. Mod. Phys. by the author, it incorporates
surface growth classes, classes of spin models, percolation and
multi-component system classes as well as damage spreading
transitions. (The success of that review can be quantified by the
more than one hundred independent citations of that paper since
2004.)
The extensions in this book include new topics like local scale
invariance,
uncritical points, phase space topologies, nonperturbative
renormalization group results and disordered systems that are
discussed in more detail. This book also aims to be more
pedagogical, providing more background and derivation of results.
Topological phase space diagrams introduced by Kamenev
(Physical
Reviť» E
2006)
very recentlv are used as a guide for
one-component, reaction-diffusion sv stems. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Ódor, Géza 1960- |
| author_GND | (DE-588)136693814 |
| author_facet | Ódor, Géza 1960- |
| author_role | aut |
| author_sort | Ódor, Géza 1960- |
| author_variant | g ó gó |
| building | Verbundindex |
| bvnumber | BV035166573 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.85.S34 |
| callnumber-search | QC174.85.S34 |
| callnumber-sort | QC 3174.85 S34 |
| callnumber-subject | QC - Physics |
| classification_rvk | UG 2000 UG 3500 UG 3800 |
| ctrlnum | (OCoLC)225820401 (DE-599)BVBBV035166573 |
| dewey-full | 530.15/95 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15/95 |
| dewey-search | 530.15/95 |
| dewey-sort | 3530.15 295 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| id | DE-604.BV035166573 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:52:43Z |
| indexdate | 2024-07-09T21:26:30Z |
| institution | BVB |
| isbn | 981281227X 9789812812278 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016973592 |
| oclc_num | 225820401 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-20 DE-703 DE-11 DE-19 DE-BY-UBM |
| physical | XIX, 276 S. Ill., graph. Darst. 24 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Ódor, Géza 1960- Verfasser (DE-588)136693814 aut Universality in nonequilibrium lattice systems theoretical foundations Géza Ódor Hackensack, NJ [u.a.] World Scientific 2008 XIX, 276 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Scaling laws (Statistical physics) Lattice theory Self-organizing systems Phase transformations (Statistical physics) Differentiable dynamical systems Gittermodell (DE-588)4226961-1 gnd rswk-swf Universalität (DE-588)4186918-7 gnd rswk-swf Nichtgleichgewicht (DE-588)4171730-2 gnd rswk-swf Gittermodell (DE-588)4226961-1 s Nichtgleichgewicht (DE-588)4171730-2 s Universalität (DE-588)4186918-7 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016973592&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016973592&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Ódor, Géza 1960- Universality in nonequilibrium lattice systems theoretical foundations Scaling laws (Statistical physics) Lattice theory Self-organizing systems Phase transformations (Statistical physics) Differentiable dynamical systems Gittermodell (DE-588)4226961-1 gnd Universalität (DE-588)4186918-7 gnd Nichtgleichgewicht (DE-588)4171730-2 gnd |
| subject_GND | (DE-588)4226961-1 (DE-588)4186918-7 (DE-588)4171730-2 |
| title | Universality in nonequilibrium lattice systems theoretical foundations |
| title_auth | Universality in nonequilibrium lattice systems theoretical foundations |
| title_exact_search | Universality in nonequilibrium lattice systems theoretical foundations |
| title_exact_search_txtP | Universality in nonequilibrium lattice systems theoretical foundations |
| title_full | Universality in nonequilibrium lattice systems theoretical foundations Géza Ódor |
| title_fullStr | Universality in nonequilibrium lattice systems theoretical foundations Géza Ódor |
| title_full_unstemmed | Universality in nonequilibrium lattice systems theoretical foundations Géza Ódor |
| title_short | Universality in nonequilibrium lattice systems |
| title_sort | universality in nonequilibrium lattice systems theoretical foundations |
| title_sub | theoretical foundations |
| topic | Scaling laws (Statistical physics) Lattice theory Self-organizing systems Phase transformations (Statistical physics) Differentiable dynamical systems Gittermodell (DE-588)4226961-1 gnd Universalität (DE-588)4186918-7 gnd Nichtgleichgewicht (DE-588)4171730-2 gnd |
| topic_facet | Scaling laws (Statistical physics) Lattice theory Self-organizing systems Phase transformations (Statistical physics) Differentiable dynamical systems Gittermodell Universalität Nichtgleichgewicht |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016973592&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016973592&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT odorgeza universalityinnonequilibriumlatticesystemstheoreticalfoundations |