Sequential Cavity Method for Computing Free Energy and Surface Pressure
We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models on a lattice Zd [Z superscript d]. Our method is based on representing the free energy and surface pressure in terms of certain marginal probabilities in a suitably modi...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
2011
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| Online Access: | http://hdl.handle.net/1721.1/65918 https://orcid.org/0000-0001-8898-8778 |
| _version_ | 1826196054016524288 |
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| author | Gamarnik, David Katz, Dmitriy |
| author2 | Massachusetts Institute of Technology. Operations Research Center |
| author_facet | Massachusetts Institute of Technology. Operations Research Center Gamarnik, David Katz, Dmitriy |
| author_sort | Gamarnik, David |
| collection | MIT |
| description | We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models on a
lattice Zd [Z superscript d]. Our method is based on representing the free energy and
surface pressure in terms of certain marginal probabilities in a suitably
modi ed sublattice of Zd [Z superscript d]. Then recent deterministic algorithms for computing marginal probabilities are used to obtain numerical estimates of
the quantities of interest. The method works under the assumption of
Strong Spatial Mixing (SSP), which is a form of a correlation decay.
We illustrate our method for the hard-core and monomer-dimer models, and improve several earlier estimates. For example we show that the
exponent of the monomer-dimer coverings of Z3 [Z superscript 3] belongs to the interval
[0:78595; 0:78599], improving best previously known estimate of (approx-
imately) [0:7850; 0:7862] obtained in [FP05],[FKLM]. Moreover, we show
that given a target additive error e [epsilon] > 0, the computational e ffort of our
method for these two models is (1=e)O(1) [(1 / epsilon) superscript 0(1)] both for free energy and surface
pressure. In contrast, prior methods, such as transfer matrix method,
require exp ((1/e)0/1) [((1 / epsilon) superscript 0(1))]
computation e ffort. |
| first_indexed | 2024-09-23T10:20:08Z |
| format | Article |
| id | mit-1721.1/65918 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:20:08Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | mit-1721.1/659182022-09-26T17:17:39Z Sequential Cavity Method for Computing Free Energy and Surface Pressure Gamarnik, David Katz, Dmitriy Massachusetts Institute of Technology. Operations Research Center Sloan School of Management Gamarnik, David Gamarnik, David Katz, Dmitriy We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models on a lattice Zd [Z superscript d]. Our method is based on representing the free energy and surface pressure in terms of certain marginal probabilities in a suitably modi ed sublattice of Zd [Z superscript d]. Then recent deterministic algorithms for computing marginal probabilities are used to obtain numerical estimates of the quantities of interest. The method works under the assumption of Strong Spatial Mixing (SSP), which is a form of a correlation decay. We illustrate our method for the hard-core and monomer-dimer models, and improve several earlier estimates. For example we show that the exponent of the monomer-dimer coverings of Z3 [Z superscript 3] belongs to the interval [0:78595; 0:78599], improving best previously known estimate of (approx- imately) [0:7850; 0:7862] obtained in [FP05],[FKLM]. Moreover, we show that given a target additive error e [epsilon] > 0, the computational e ffort of our method for these two models is (1=e)O(1) [(1 / epsilon) superscript 0(1)] both for free energy and surface pressure. In contrast, prior methods, such as transfer matrix method, require exp ((1/e)0/1) [((1 / epsilon) superscript 0(1))] computation e ffort. 2011-09-21T20:28:04Z 2011-09-21T20:28:04Z 2009-10 2009-05 Article http://purl.org/eprint/type/JournalArticle 0022-4715 http://hdl.handle.net/1721.1/65918 Gamarnik, David, and Dmitriy Katz. “Sequential Cavity Method for Computing Free Energy and Surface Pressure.” Journal of Statistical Physics 137.2 (2009) : 205-232. Copyright © 2009, Springer Science+Business Media, LLC https://orcid.org/0000-0001-8898-8778 en_US http://dx.doi.org/10.1007/s10955-009-9849-3 Journal of Statistical Physics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Prof. Gamarnik via Alex Caracuzzo |
| spellingShingle | Gamarnik, David Katz, Dmitriy Sequential Cavity Method for Computing Free Energy and Surface Pressure |
| title | Sequential Cavity Method for Computing Free Energy and Surface Pressure |
| title_full | Sequential Cavity Method for Computing Free Energy and Surface Pressure |
| title_fullStr | Sequential Cavity Method for Computing Free Energy and Surface Pressure |
| title_full_unstemmed | Sequential Cavity Method for Computing Free Energy and Surface Pressure |
| title_short | Sequential Cavity Method for Computing Free Energy and Surface Pressure |
| title_sort | sequential cavity method for computing free energy and surface pressure |
| url | http://hdl.handle.net/1721.1/65918 https://orcid.org/0000-0001-8898-8778 |
| work_keys_str_mv | AT gamarnikdavid sequentialcavitymethodforcomputingfreeenergyandsurfacepressure AT katzdmitriy sequentialcavitymethodforcomputingfreeenergyandsurfacepressure |