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arXiv · 2010.07423

An exactly solvable ansatz for statistical mechanics models

Isaac H. Kim
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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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Isaac H. Kim. 2020-10-14. An exactly solvable ansatz for statistical mechanics models. https://doi.org/10.1088/1742-5468%2Fac0152

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