Infinite randomness and quantum Griffiths effects in a classical system: the randomly layered Heisenberg magnet

TL;DR

This paper studies a three-dimensional classical Heisenberg magnet with planar defects, revealing an exotic infinite-randomness critical point with Griffiths effects and extremely slow dynamics, using a strong-disorder renormalization group approach.

Contribution

It demonstrates the presence of infinite-randomness criticality and Griffiths effects in a classical system with planar disorder, extending quantum critical phenomena concepts.

Findings

Infinite-randomness critical point identified

Strong Griffiths singularities observed

Critical dynamics are extremely slow, with logarithmic decay

Abstract

We investigate the phase transition in a three-dimensional classical Heisenberg magnet with planar defects, i.e., disorder perfectly correlated in two dimensions. By applying a strong-disorder renormalization group, we show that the critical point has exotic infinite-randomness character. It is accompanied by strong power-law Griffiths singularities. We compute various thermodynamic observables paying particular attention to finite-size effects relevant for an experimental verification of our theory. We also study the critical dynamics within a Langevin equation approach and find it extremely slow. At the critical point, the autocorrelation function decays only logarithmically with time while it follows a nonuniversal power-law in the Griffiths phase.