How to Compute Loop Corrections to Bethe Approximation
统计力学
2009-11-11 v1 无序系统与神经网络
摘要
We introduce a method for computing corrections to Bethe approximation for spin models on arbitrary lattices. Unlike cluster variational methods, the new approach takes into account fluctuations on all length scales. The derivation of the leading correction is explained and applied to two simple examples: the ferromagnetic Ising model on d-dimensional lattices, and the spin glass on random graphs (both in their high-temperature phases). In the first case we rederive the well-known Ginzburg criterion and the upper critical dimension. In the second, we compute finite-size corrections to the free energy.
引用
@article{arxiv.cond-mat/0506769,
title = {How to Compute Loop Corrections to Bethe Approximation},
author = {Andrea Montanari and Tommaso Rizzo},
journal= {arXiv preprint arXiv:cond-mat/0506769},
year = {2009}
}
备注
16 pages, 2 eps figures