Two-dimensional Ising model with self-dual biaxially correlated disorder

TL;DR

This study investigates the critical behavior of the 2D Ising model with biaxially correlated disorder fixed by self-duality, revealing altered critical exponents and conformal properties through large-scale Monte Carlo simulations.

Contribution

It provides the first detailed numerical analysis of the 2D Ising model with biaxially correlated disorder fixed by self-duality, highlighting its impact on critical exponents and conformal invariance.

Findings

Correlation length exponent =2.005(5) matches isotropic long-range disorder predictions.

Magnetization scaling dimension x_m=0.1294(7) is larger than in the pure system.

Conformal profiles of magnetization and energy density are numerically consistent with theoretical expectations.

Abstract

We consider the Ising model on the square lattice with biaxially correlated random ferromagnetic couplings, the critical point of which is fixed by self-duality. The disorder represents a relevant perturbation according to the extended Harris criterion. Critical properties of the system are studied by large scale Monte Carlo simulations. The correlation length critical exponent, \nu=2.005(5), corresponds to that expected in a system with isotropic correlated long-range disorder, whereas the scaling dimension of the magnetization density, x_m=0.1294(7), is somewhat larger than in the pure system. Conformal properties of the magnetization and energy density profiles are also examined numerically.