Lage-Castellanos Alejandro, Mulet Roberto, Ricci-Tersenghi Federico, Rizzo Tommaso
Department of Theoretical Physics and Henri-Poincaré Group of Complex Systems, Physics Faculty, University of Havana, La Habana, Codigo Postal 10400, Cuba.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Oct;84(4 Pt 2):046706. doi: 10.1103/PhysRevE.84.046706. Epub 2011 Oct 24.
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 two-dimensional (2D) Edwards-Anderson (EA) model] we propose a message-passing algorithm--the dual algorithm--to estimate the marginal probabilities of spin glasses on finite-dimensional lattices. We use the EA models in 2D and 3D as benchmarks. The dual algorithm improves the Bethe approximation, and we show that in a wide range of temperatures (compared to the Bethe critical temperature) 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. In 2D and 3D the quality of the inference deteriorates only where the correlation length becomes very large, i.e., at low temperatures in 2D and close to the critical temperature in 3D.
从簇变分方法出发，并受顺磁假设正确性的启发（一般在高温下，以及在二维（2D）爱德华兹 - 安德森（EA）模型中的任何温度下），我们提出了一种消息传递算法——对偶算法——来估计有限维晶格上自旋玻璃的边际概率。我们使用二维和三维的EA模型作为基准。对偶算法改进了贝叶斯近似，并且我们表明，在很宽的温度范围内（与贝叶斯临界温度相比），我们的算法与蒙特卡罗模拟、双环算法以及对具有双峰和高斯相互作用的二维系统基态的精确计算相比，表现得非常好。此外，它通常比其他可证明收敛的方法（如双环算法）快100倍。在二维和三维中，只有在关联长度变得非常大的地方，即二维中的低温和三维中接近临界温度时，推理的质量才会变差。
