Polynomial-time approximation algorithms for the Ising model:
Abstract: "The paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any specified degree of accuracy. The running time of the algorithm increases only polynomially with the size of the system (i.e., the number of sites) and a...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Edinburgh
1990
|
| Edition: | Revised |
| Series: | University <Edinburgh> / Department of Computer Science: CSR
1 |
| Subjects: | |
| Summary: | Abstract: "The paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any specified degree of accuracy. The running time of the algorithm increases only polynomially with the size of the system (i.e., the number of sites) and a parameter which controls the accuracy of the result. Further approximation algorithms are presented for the mean energy and the mean magnetic moment of ferromagnetic Ising systems. The algorithms are based on Monte Carlo simulation of a suitably defined ergodic Markov chain. The states of the chain are not, as is customary, Ising spin configurations, but spanning subgraphs of the interaction graph of the system. It is shown that the expectations of simple operators on these configurations give numerical information about the partition function and related quantities The performance guarantees for the algorithms are rigorously derived, and rest on the fact that the Markov chain in question is rapidly mixing, i.e., converges to its equilibrium distribution in a polynomial number of steps. This is apparently the first time that rapid mixing has been demonstrated at all temperatures for a Markov chain related to the Ising problem. |
| Physical Description: | 38 S. |
Staff View
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| 245 | 1 | 0 | |a Polynomial-time approximation algorithms for the Ising model |c Mark Jerrum and Alistair Sinclair |
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| 490 | 1 | |a University <Edinburgh> / Department of Computer Science: CSR |v 1 | |
| 520 | 3 | |a Abstract: "The paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any specified degree of accuracy. The running time of the algorithm increases only polynomially with the size of the system (i.e., the number of sites) and a parameter which controls the accuracy of the result. Further approximation algorithms are presented for the mean energy and the mean magnetic moment of ferromagnetic Ising systems. The algorithms are based on Monte Carlo simulation of a suitably defined ergodic Markov chain. The states of the chain are not, as is customary, Ising spin configurations, but spanning subgraphs of the interaction graph of the system. It is shown that the expectations of simple operators on these configurations give numerical information about the partition function and related quantities | |
| 520 | 3 | |a The performance guarantees for the algorithms are rigorously derived, and rest on the fact that the Markov chain in question is rapidly mixing, i.e., converges to its equilibrium distribution in a polynomial number of steps. This is apparently the first time that rapid mixing has been demonstrated at all temperatures for a Markov chain related to the Ising problem. | |
| 650 | 7 | |a Solid state physics and magnetism |2 sigle | |
| 650 | 7 | |a Theoretical physics |2 sigle | |
| 650 | 4 | |a Ferromagnetism | |
| 650 | 4 | |a Ising model | |
| 700 | 1 | |a Sinclair, Alistair |e Verfasser |4 aut | |
| 810 | 2 | |a Department of Computer Science: CSR |t University <Edinburgh> |v 1 |w (DE-604)BV008906637 |9 1 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-005905489 | ||
Record in the Search Index
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| author | Jerrum, Mark 1955- Sinclair, Alistair |
| author_GND | (DE-588)12443133X |
| author_facet | Jerrum, Mark 1955- Sinclair, Alistair |
| author_role | aut aut |
| author_sort | Jerrum, Mark 1955- |
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| building | Verbundindex |
| bvnumber | BV008949865 |
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| ctrlnum | (OCoLC)22366489 (DE-599)BVBBV008949865 |
| discipline | Informatik |
| edition | Revised |
| format | Book |
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| id | DE-604.BV008949865 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:27:18Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005905489 |
| oclc_num | 22366489 |
| open_access_boolean | |
| owner | DE-29T DE-91G DE-BY-TUM |
| owner_facet | DE-29T DE-91G DE-BY-TUM |
| physical | 38 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| record_format | marc |
| series2 | University <Edinburgh> / Department of Computer Science: CSR |
| spelling | Jerrum, Mark 1955- Verfasser (DE-588)12443133X aut Polynomial-time approximation algorithms for the Ising model Mark Jerrum and Alistair Sinclair Revised Edinburgh 1990 38 S. txt rdacontent n rdamedia nc rdacarrier University <Edinburgh> / Department of Computer Science: CSR 1 Abstract: "The paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any specified degree of accuracy. The running time of the algorithm increases only polynomially with the size of the system (i.e., the number of sites) and a parameter which controls the accuracy of the result. Further approximation algorithms are presented for the mean energy and the mean magnetic moment of ferromagnetic Ising systems. The algorithms are based on Monte Carlo simulation of a suitably defined ergodic Markov chain. The states of the chain are not, as is customary, Ising spin configurations, but spanning subgraphs of the interaction graph of the system. It is shown that the expectations of simple operators on these configurations give numerical information about the partition function and related quantities The performance guarantees for the algorithms are rigorously derived, and rest on the fact that the Markov chain in question is rapidly mixing, i.e., converges to its equilibrium distribution in a polynomial number of steps. This is apparently the first time that rapid mixing has been demonstrated at all temperatures for a Markov chain related to the Ising problem. Solid state physics and magnetism sigle Theoretical physics sigle Ferromagnetism Ising model Sinclair, Alistair Verfasser aut Department of Computer Science: CSR University <Edinburgh> 1 (DE-604)BV008906637 1 |
| spellingShingle | Jerrum, Mark 1955- Sinclair, Alistair Polynomial-time approximation algorithms for the Ising model Solid state physics and magnetism sigle Theoretical physics sigle Ferromagnetism Ising model |
| title | Polynomial-time approximation algorithms for the Ising model |
| title_auth | Polynomial-time approximation algorithms for the Ising model |
| title_exact_search | Polynomial-time approximation algorithms for the Ising model |
| title_full | Polynomial-time approximation algorithms for the Ising model Mark Jerrum and Alistair Sinclair |
| title_fullStr | Polynomial-time approximation algorithms for the Ising model Mark Jerrum and Alistair Sinclair |
| title_full_unstemmed | Polynomial-time approximation algorithms for the Ising model Mark Jerrum and Alistair Sinclair |
| title_short | Polynomial-time approximation algorithms for the Ising model |
| title_sort | polynomial time approximation algorithms for the ising model |
| topic | Solid state physics and magnetism sigle Theoretical physics sigle Ferromagnetism Ising model |
| topic_facet | Solid state physics and magnetism Theoretical physics Ferromagnetism Ising model |
| volume_link | (DE-604)BV008906637 |
| work_keys_str_mv | AT jerrummark polynomialtimeapproximationalgorithmsfortheisingmodel AT sinclairalistair polynomialtimeapproximationalgorithmsfortheisingmodel |