Optimal Real-Space Renormalization-Group Transformations with Artificial Neural Networks

2019/12/19 by Chung, Jui-Hui, Kao, Ying-Jer
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.1912.09005

Abstract

We introduce a general method for optimizing real-space renormalization-group transformations to study the critical properties of a classical system. The scheme is based on minimizing the Kullback-Leibler divergence between the distribution of the system and the normalized normalizing factor of the transformation parametrized by a restricted Boltzmann machine. We compute the thermal critical exponent of the two-dimensional Ising model using the trained optimal projector and obtain a very accurate thermal critical exponent y_t=1.0001(11) after the first step of the transformation.

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