Thermal fluctuations and phase diagrams of the phase field crystal model with pinning

TL;DR

This study explores how thermal fluctuations affect the phase diagram of a two-dimensional phase field crystal model with pinning, revealing complex phases and critical behavior consistent with the Ising universality class.

Contribution

It introduces a non-conserved version of the model and uses Monte Carlo simulations to map the phase diagram considering thermal effects and pinning.

Findings

Rich phase diagram with multiple phases

Thermal melting transition aligns with Ising universality class

Finite-size scaling confirms critical exponents

Abstract

We study the influence of thermal fluctuations in the phase diagram of a recently introduced two-dimensional phase field crystal model with an external pinning potential. The model provides a continuum description of pinned lattice systems allowing for both elastic deformations and topological defects. We introduce a non-conserved version of the model and determine the ground-state phase diagram as a function of lattice mismatch and strength of the pinning potential. Monte Carlo simulations are used to determine the phase diagram as a function of temperature near commensurate phases. The results show a rich phase diagram with commensurate, incommensurate and liquid-like phases with a topology strongly dependent on the type of ordered structure. A finite-size scaling analysis of the melting transition for the $c(2 \times 2)$ commensurate phase shows that the thermal correlation length exponent $\nu$ and specific heat behavior are consistent with the Ising universality class as expected from analytical arguments.