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

Jui-Hui Chung¹, Ying-Jer Kao^1*

¹Physics, National Taiwan University, Taiwan

* Presenter:Ying-Jer Kao, email:yjkao@phys.ntu.edu.tw

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 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 exponent y_t = 1.0001(11) after the first step of the transformation.

Keywords: restricted Boltzmann machine, renormalization group, critical exponenets