论文标题
统计力学模型的准确解决的ANSATZ
An exactly solvable ansatz for statistical mechanics models
论文作者
论文摘要
我们提出了一个“确切可解决”概率分布的家族，以对二维统计力学模型的近似分区函数。尽管这些分布严格存在于平均场框架之外，但可以在与系统大小线性缩放的时间内计算其自由能。该结构基于对边际问题的简单但非平凡的解决方案。我们对局部一致的边缘概率集合（i）确保存在一致的全局概率分布，并且（ii）导致最大全局熵的精确表达式。
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.
