Evidence for power-law Griffiths singularities in a layered Heisenberg magnet

TL;DR

This paper provides numerical Monte-Carlo evidence supporting the existence of infinite-randomness critical points and power-law Griffiths singularities in a layered Heisenberg magnet, confirming theoretical predictions.

Contribution

It offers the first numerical confirmation of the predicted exotic critical behavior and Griffiths singularities in a disordered layered Heisenberg model.

Findings

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

Spin autocorrelation decays very slowly following a non-universal power law.

Supports the strong-disorder renormalization group predictions.

Abstract

We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent strong-disorder renormalization group approach [Phys. Rev. B 81, 144407 (2010)] predicted that the critical point in this system is of exotic infinite-randomness type and is accompanied by strong power-law Griffiths singularities. Here, we report results of Monte-Carlo simulations that provide numerical evidence in support of these predictions. 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. In addition, we calculate the time autocorrelation function of the spins. It features a very slow decay in the Griffiths phase, following a non-universal power law in time.