Critical correlations of Ising and Yang-Lee critical points from Tensor RG

TL;DR

This paper demonstrates that tensor renormalization group (TRG) can accurately estimate universal critical data for 2D Ising and Yang-Lee models, achieving high precision with moderate computational effort.

Contribution

The study shows that TRG effectively computes critical exponents and amplitude ratios for various 2D critical points, with improved accuracy at higher bond dimensions.

Findings

TRG yields results within 1% of known values at bond dimension 28.

Performance improves rapidly with bond dimension, especially for anisotropic and Yang-Lee models.

TRG compares favorably to Monte Carlo in terms of computational cost and accuracy.

Abstract

We examine feasibility of accurate estimations of universal critical data using tensor renormalization group (TRG) algorithm introduced by Levin and Nave. Specifically, we compute critical exponents $\gamma, \gamma/\nu, \delta, \eta$ and amplitude ratio $A$ for the magnetic susceptibility from one- and two-point correlation functions for three critical points in two dimensions -- isotropic and anisotropic Ising models and the Yang-Lee critical point at finite imaginary magnetic field. While TRG performs quantitaviely well in all three cases already at smaller bond dimension, $D=16$, the latter two appear to show more rapid improvement in bond dimension, e.g. we are able to reproduce exactly known results to better than one percent at bond dimension $D=24$. We are able to reproduce exactly known values to better than 1 percent with modest effort of bond dimension 28. We comment on the relationship between these results and earlier results on conformal dimensions, fixed points of tensor RG, and also compare computational costs of tensor renormalization vs. conventional Monte-Carlo sampling.