有限维自旋玻璃的快速推理算法：对偶格点上的置信传播
A very fast inference algorithm for finite-dimensional spin glasses: Belief Propagation on the dual lattice
摘要：
本文从集团变分方法出发，受顺磁近似的正确性（在一般高温下，以及在二维Edwards-Anderson模型中的任意温度下）的启发，提出了一种新的信息传递算法--对偶算法，用于估计有限维晶格上自旋玻璃的边缘概率.我们表明，在很宽的温度范围内，我们的算法比较非常好的蒙特卡罗模拟，与双环算法和精确计算的基态的二维系统与双峰和高斯相互作用。而且它通常比其他可证明收敛的方法快100倍，如双环算法。
英文摘要：
Starting from a Cluster Variational Method, and inspired by the correctness of the paramagnetic Ansatz (at high temperatures in general, and at any temperature in the 2D Edwards-Anderson model) we propose a novel message passing algorithm --- the Dual algorithm --- to estimate the marginal probabilities of spin glasses on finite dimensional lattices. We show that in a wide range of temperatures our algorithm compares very well with Monte Carlo simulations, with the Double Loop algorithm and with exact calculation of the ground state of 2D systems with bimodal and Gaussian interactions. Moreover it is usually 100 times faster than other provably convergent methods, as the Double Loop algorithm.
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