Neural Monte Carlo Renormalization Group

Understand

The key idea behind the renormalization group (RG) transformation is that properties of physical systems with very different microscopic makeups can be characterized by a few universal parameters.

• However, finding the optimal RG transformation remains difficult due to the many possible choices of the weight factors in the RG procedure.
• Here we show, by identifying the conditional distribution in the restricted Boltzmann machine (RBM) and the weight factor distribution in the RG procedure, an optimal real-space RG transformation can be learned without prior knowledge of the physical system.
• This neural Monte Carlo RG algorithm allows for direct computation of the RG flow and critical exponents.