Dynamics at a smeared phase transition

TL;DR

This paper explores how rare regions influence the slow dynamics of disordered Ising magnets with planar defects, revealing a smeared phase transition with unique decay behaviors in autocorrelation functions.

Contribution

It combines numerical solutions and scaling arguments to analyze dynamics beyond mean-field theory in systems with correlated disorder, highlighting novel slow decay phenomena.

Findings

Autocorrelation decays as a stretched exponential at intermediate times.

Dynamics in the tail region are slower than in Griffiths phases.

Late-time behavior follows a power-law decay.

Abstract

We investigate the effects of rare regions on the dynamics of Ising magnets with planar defects, i.e., disorder perfectly correlated in two dimensions. In these systems, the magnetic phase transition is smeared because static long-range order can develop on isolated rare regions. We first study an infinite-range model by numerically solving local dynamic mean-field equations. Then we use extremal statistics and scaling arguments to discuss the dynamics beyond mean-field theory. In the tail region of the smeared transition the dynamics is even slower than in a conventional Griffiths phase: the spin autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small equilibrium value following a power law at late times.