Infinite-randomness criticality in a randomly layered Heisenberg magnet

TL;DR

This study uses large-scale Monte Carlo simulations to provide numerical evidence for infinite-randomness criticality in a randomly layered Heisenberg magnet, revealing unique scaling behaviors and anomalous elasticity in the Griffiths phase.

Contribution

It offers the first numerical confirmation of the infinite-randomness scenario in a Heisenberg magnet, detailing critical and Griffiths phase properties.

Findings

Magnetic susceptibility diverges with a non-universal power law in the Griffiths phase.

Parallel spin-wave stiffness remains nonzero below T_c, while perpendicular stiffness can be zero.

In-plane correlation length diverges inside the disordered phase at T > T_c.

Abstract

We study the ferromagnetic phase transition in a randomly layered Heisenberg magnet using large-scale Monte-Carlo simulations. Our results provide numerical evidence for the infinite-randomness scenario recently predicted within a {strong-disorder renormalization group approach}. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. We also study the perpendicular and parallel spin-wave stiffnesses in the Griffiths phase. In agreement with the theoretical predictions, the parallel stiffness is nonzero for all temperatures $T<T_c$. In contrast, the perpendicular stiffness remains zero in part of the ordered phase, giving rise to anomalous elasticity. In addition, we calculate the in-plane correlation length which diverges already inside the disordered phase at a temperature significantly higher than $T_c$. The time autocorrelation function within model $A$ dynamics displays an ultraslow logarithmic decay at criticality and a nonuniversal power-law in the Griffiths phase.