Anomalous ordering in inhomogeneously strained materials

TL;DR

This paper investigates a continuous phase transition in an inhomogeneously strained material model, revealing universal critical exponents similar to those in various physical systems, suggesting common underlying physics.

Contribution

It provides the first Monte Carlo simulation analysis of critical exponents in a model of inhomogeneously strained materials, linking them to universal behavior across different systems.

Findings

Critical exponents: beta=0.18, gamma=1.0, alpha=0.10

Exponents comparable to those in magnetic and structural transitions

Transition related to surface phenomena despite no free surface

Abstract

We study a continuous quasi-two-dimensional order-disorder phase transition that occurs in a simple model of a material that is inhomogeneously strained due to the presence of dislocation lines. Performing Monte Carlo simulations of different system sizes and using finite size scaling, we measure critical exponents describing the transition of beta=0.18\pm0.02, gamma=1.0\pm0.1, and alpha=0.10\pm0.02. Comparable exponents have been reported in a variety of physical systems. These systems undergo a range of different types of phase transitions, including structural transitions, exciton percolation, and magnetic ordering. In particular, similar exponents have been found to describe the development of magnetic order at the onset of the pseudogap transition in high-temperature superconductors. Their common universal critical exponents suggest that the essential physics of the transition in all of these physical systems is the same as in our model. We argue that the nature of the transition in our model is related to surface transitions, although our model has no free surface.