Improved Actions using The Renormalization Group

TL;DR

This paper presents a numerical approach combining tensor renormalization group ideas with Monte Carlo simulations to efficiently analyze critical phenomena in phase transitions, demonstrated on the 3D XY model.

Contribution

It introduces an improved action method that enhances the study of critical properties near phase transitions using smaller system sizes.

Findings

Effective in extracting critical properties with reduced computational effort

Applicable to classical and quantum phase transitions

Demonstrated success on the 3D XY model

Abstract

We introduce a numerical method to study critical properties near classical and quantum phase transitions. Our method applies ideas of the Tensor Renormalization Group to obtain an improved action which is used to extract critical properties by performing Monte Carlo simulations on relatively small system sizes. We demonstrate this method on the XY model in three dimensions. Our method may provide a framework with which to efficiently study universal properties in a large class of phase transitions.