Phase Transitions in a Modified Ising Spin Glass Model: A Tensor-Network-based Sampling Approach

TL;DR

This paper introduces a tensor-network-based sampling method to study phase transitions in a modified Ising spin glass model, revealing a separated spin-glass and ferromagnetic transition and a distinct universality class.

Contribution

The authors develop a hierarchical sampling scheme enabling high-precision analysis of a modified Nishimori model on large lattices, providing new insights into phase transition behavior.

Findings

Spin-glass and ferromagnetic transitions are separated on the Nishimori line.

Evidence supports an intermediate Mattis-like spin-glass phase.

Transitions have a different universality class from the standard EA model.

Abstract

Phase transitions in a modified Nishimori model, including the model considered by Kitatani, on a two-dimensional square lattice are investigated using a tensor-network-based sampling scheme. In this model, generating bond configurations is computationally demanding because of the correlated random interactions. The employed sampling method enables hierarchical and independent sampling of both bonds and spins. This approach allows high-precision calculations for system sizes up to $L=256$. The results provide clear numerical evidence that the spin-glass and ferromagnetic transitions are separated on the Nishimori line, supporting the existence of an intermediate Mattis-like spin-glass phase. This finding is consistent with the reentrant transition numerically observed in the two-dimensional Edwards-Anderson (EA) model. Furthermore, critical exponents estimated via finite-size-scaling analysis indicate that the universality class of the transitions differs from that of the standard independent and identically distributed EA model.