Smeared phase transition in a three-dimensional Ising model with planar defects: Monte-Carlo simulations

TL;DR

This paper uses large-scale Monte Carlo simulations to demonstrate that a three-dimensional Ising model with planar defects exhibits a smeared phase transition, where different regions order at different temperatures due to correlated disorder.

Contribution

It provides the first detailed simulation evidence of smeared phase transitions in a 3D Ising model with planar defects, confirming recent theoretical predictions.

Findings

Phase transition is smeared with no single critical temperature.

Rare regions can develop long-range order before the bulk.

Simulation results agree with extremal statistics theory.

Abstract

We present results of large-scale Monte Carlo simulations for a three-dimensional Ising model with short range interactions and planar defects, i.e., disorder perfectly correlated in two dimensions. We show that the phase transition in this system is smeared, i.e., there is no single critical temperature, but different parts of the system order at different temperatures. This is caused by effects similar to but stronger than Griffiths phenomena. In an infinite-size sample there is an exponentially small but finite probability to find an arbitrary large region devoid of impurities. Such a rare region can develop true long-range order while the bulk system is still in the disordered phase. We compute the thermodynamic magnetization and its finite-size effects, the local magnetization, and the probability distribution of the ordering temperatures for different samples. Our Monte-Carlo results are in good agreement with a recent theory based on extremal statistics.