Monte Carlo Renormalization Group Analysis of Lattice $\phi^4$ Model in $D=3,4$

TL;DR

This paper introduces a Monte Carlo renormalization group method to analyze critical phenomena in lattice $^4$ models, successfully reproducing theoretical behavior in 3D and 4D, and adaptable to complex models.

Contribution

The paper presents a new Monte Carlo RG approach that effectively captures flow diagrams in lattice $^4$ models and is applicable to more complex systems.

Findings

Renormalization flow diagrams match theoretical predictions.

Method successfully applied to 3D and 4D lattice $^4$ models.

Potential for application to frustrated spin models.

Abstract

We present a simple, sophisticated method to capture renormalization group flow in Monte Carlo simulation, which provides important information of critical phenomena. We applied the method to $D=3,4$ lattice $\phi^4$ model and obtained renormalization flow diagram which well reproduces theoretically predicted behavior of continuum $\phi^4$ model. We also show that the method can be easily applied to much more complicated models, such as frustrated spin models.