An exactly solvable ansatz for statistical mechanics models

• URL: http://arxiv.org/abs/2010.07423v1
• Date: Wed, 14 Oct 2020 22:30:22 GMT
• Title: An exactly solvable ansatz for statistical mechanics models
• Authors: Isaac H. Kim
• Abstract summary: We propose a family of "exactly solvable" probability distributions to approximate partition functions of two-dimensional statistical mechanics models. The distributions lie strictly outside the mean-field framework, but their free energies can be computed in a time that scales linearly with the system size.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a family of "exactly solvable" probability distributions to approximate partition functions of two-dimensional statistical mechanics models. While these distributions lie strictly outside the mean-field framework, their free energies can be computed in a time that scales linearly with the system size. This construction is based on a simple but nontrivial solution to the marginal problem. We formulate two non-linear constraints on the set of locally consistent marginal probabilities that simultaneously (i) ensure the existence of a consistent global probability distribution and (ii) lead to an exact expression for the maximum global entropy.

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