Topological invariant tensor renormalization group method for spin glasses

TL;DR

This paper introduces a topological invariant tensor renormalization group method to analyze 2D spin glasses, accurately predicting critical points and outperforming mean field methods, with potential applications to 3D systems.

Contribution

It develops a novel topological invariant TRG scheme for disordered spin glasses, providing improved accuracy in calculating critical points and correlations over existing methods.

Findings

Accurately predicts the Nishimori multi-critical point.

Outperforms mean field methods in partition function calculations.

Potential to extend to three-dimensional spin glass systems.

Abstract

Tensor renormalization group method (TRG) is a real space renormalization group approach. It has been successfully applied to both classical and quantum systems. In this paper, we study a disordered and frustrated system, the two-dimensional Edward-Anderson model, by a new topological invariant TRG scheme. We propose an approach to calculate the local magnetizations and nearest pair correlations simultaneously. The Nishimori multi-critical point predicted by the topological invariant TRG agrees well with the recent Monte-Carlo results. The TRG schemes outperform the mean field methods on the calculation of the partition function. We notice that it maybe obtain a negative partition function at sufficiently low temperatures. However, the negative contribution can be neglected if the systems is large enough. This topological invariant TRG can also be used to study three-dimensional spin glass systems.