Smearing of the phase transition in Ising systems with planar defects

TL;DR

This paper demonstrates that phase transitions in Ising models with planar defects are smeared due to rare regions developing static order, leading to inhomogeneous order parameters and exponential temperature dependence.

Contribution

It provides a theoretical and computational analysis showing how planar defects cause smearing of phase transitions, extending Griffiths phenomena effects.

Findings

Phase transitions are destroyed by smearing in systems with planar defects.

Rare regions can develop static order even when the bulk is disordered.

The order parameter depends exponentially on temperature near the transition.

Abstract

We show that phase transitions in Ising systems with planar defects, i.e., disorder perfectly correlated in two dimensions are destroyed by smearing. This is caused by effects similar to but stronger than the Griffiths phenomena: Exponentially rare spatial regions can develop true static long-range order even when the bulk system is still in its disordered phase. Close to the smeared transition, the order parameter is very inhomogeneous in space, with the thermodynamic (average) order parameter depending exponentially on temperature. We determine the behavior using extremal statistics, and we illustrate the results by computer simulations.