Phase transitions in systems of magnetic dipoles on a square lattice with quenched disorder

TL;DR

This study uses Monte Carlo simulations to explore how quenched orientational disorder affects phase transitions in a square lattice of classical dipoles, revealing continuous changes in critical behavior and weak long-range order near maximum disorder.

Contribution

It introduces a detailed analysis of disorder effects on dipolar systems, showing continuous variation of critical exponents and the persistence of weak long-range order.

Findings

Second order transition between paramagnetic and antiferromagnetic phases.

Critical exponents vary continuously with disorder strength.

Weak long-range dipolar order persists below T_c at high disorder.

Abstract

We study by Monte Carlo simulations the effect of quenched orientational disorder in systems of interacting classical dipoles on a square lattice. Each dipole can lie along any of two perpendicular axes that form an angle psi with the principal axes of the lattice. We choose psi at random and without bias from the interval [-Delta, Delta] for each site of the lattice. For 0<Delta <~ pi/4 we find a thermally driven second order transition between a paramagnetic and a dipolar antiferromagnetic order phase and critical exponents that change continously with Delta. Near the case of maximum disorder Delta ~ \pi/4 we still find a second order transition at a finite temperature T_c but our results point to weak instead of {\it strong} long-ranged dipolar order for temperatures below T_c.