Correlation--function distributions at the Nishimori point of two-dimensional Ising spin glasses

TL;DR

This study uses numerical transfer-matrix methods to analyze the probability distributions of spin-spin correlations at the Nishimori point in 2D Ising spin glasses, confirming conformal invariance and examining scaling behaviors.

Contribution

It provides the first detailed numerical verification of conformal invariance and gauge symmetry effects on correlation distributions at the Nishimori point in 2D Ising spin glasses.

Findings

Conformal invariance is strictly obeyed at the Nishimori point.

Correlation distribution shapes exhibit symmetry consistent with gauge invariance.

Power law divergences in distributions near C=1 and C=0 are observed.

Abstract

The multicritical behavior at the Nishimori point of two-dimensional Ising spin glasses is investigated by using numerical transfer-matrix methods to calculate probability distributions $P(C)$ and associated moments of spin-spin correlation functions $C$ on strips. The angular dependence of the shape of correlation function distributions $P(C)$ provides a stringent test of how well they obey predictions of conformal invariance; and an even symmetry of $(1-C) P(C)$ reflects the consequences of the Ising spin-glass gauge (Nishimori) symmetry. We show that conformal invariance is obeyed in its strictest form, and the associated scaling of the moments of the distribution is examined, in order to assess the validity of a recent conjecture on the exact localization of the Nishimori point. Power law divergences of $P(C)$ are observed near C=1 and C=0, in partial accord with a simple scaling scheme which preserves the gauge symmetry.