Universality, frustration and conformal invariance in two-dimensional random Ising magnets

TL;DR

This paper investigates the critical behavior and phase transitions of two-dimensional random Ising magnets with frustration, revealing how disorder affects universality, critical exponents, and conformal invariance.

Contribution

It provides a detailed numerical analysis of frustrated 2D Ising systems, highlighting the persistence of low-temperature order and the breakdown of conformal invariance due to frustration.

Findings

Low-temperature ordering persists with pure-Ising exponents.

A vertical critical line exists at and below the Nishimori point.

Frustration induces a breakdown of conformal invariance predictions.

Abstract

We consider long, finite-width strips of Ising spins with randomly distributed couplings. Frustration is introduced by allowing both ferro- and antiferromagnetic interactions. Free energy and spin-spin correlation functions are calculated by transfer-matrix methods. Numerical derivatives and finite-size scaling concepts allow estimates of the usual critical exponents $\gamma/\nu$, $\alpha/\nu$ and $\nu$ to be obtained, whenever a second-order transition is present. Low-temperature ordering persists for suitably small concentrations of frustrated bonds, with a transition governed by pure--Ising exponents. Contrary to the unfrustrated case, subdominant terms do not fit a simple, logarithmic-enhancement form. Our analysis also suggests a vertical critical line at and below the Nishimori point. Approaching this point along either the temperature axis or the Nishimori line, one finds non-diverging specific heats. A percolation-like ratio $\gamma/\nu$ is found upon analysis of the uniform susceptibility at the Nishimori point. Our data are also consistent with frustration inducing a breakdown of the relationship between correlation-length amplitude and critical exponents, predicted by conformal invariance for pure systems.