Critical exponents at the Nishimori point

TL;DR

This paper determines the exact correlation length and crossover critical exponents at the Nishimori point of the random bond Ising model, providing new insights into fixed points with strong disorder across various dimensions.

Contribution

It presents the first exact critical exponents for frustrated random magnets at the Nishimori point, extending the analysis to higher dimensions and other models beyond Ising.

Findings

Exact correlation length exponents identified in 2D and 3D

First exact exponents for frustrated random magnets

Extension of results to higher dimensions and models

Abstract

The Nishimori point of the random bond Ising model is a prototype of renormalization group fixed points with strong disorder. We show that the exact correlation length and crossover critical exponents at this point can be identified in two and three spatial dimensions starting from properties of the Nishimori line. These are the first exact exponents for frustrated random magnets, a circumstance to be also contrasted with the fact that the exact exponents of the Ising model without disorder are not known in three dimensions. Our considerations extend to higher dimensions and models other than Ising.