Domain Wall Renormalization Group Analysis of 2-dimensional Ising Model

TL;DR

This paper applies a tensor renormalization group method to analyze the 2D Ising model, deriving fixed points, critical exponents, and temperatures with high accuracy, and explores improvements with more domain wall states.

Contribution

It introduces an explicit analytic renormalization transformation for the 2D Ising model using domain wall coarse graining, demonstrating near-exact critical parameters.

Findings

Critical temperature and exponents closely match exact values.

Explicit analytic RG transformation derived and validated.

Improvement observed with four domain wall states.

Abstract

Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the 2-dimensional square lattice. For the lowest order approximation with two domain wall states, it realizes the idea of coarse graining of domain walls. We write down explicit analytic renormalization transformation and prove that the picture of the coarse graining of the physical domain walls does hold for all physical renormalization group flows. We solve it to get the fixed point structure and obtain the critical exponents and the critical temperature. These results are very near to the exact values. We also briefly report the improvement using four domain wall states.