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 nonconserved 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 liquidlike phases with a topology strongly dependent on the type of ordered structure. A finite-size scaling analysis of the melting transition for the c(2×2) commensurate phase shows that the thermal correlation length exponent ν and specific heat behavior are consistent with the Ising universality class as expected from analytical arguments.
- order disorder phase transition
Ramos, J. A. P., Granato, E., Achim, C. V., Ying, S. C., Elder, K. R., & Ala-Nissila, T. (2008). Thermal fluctuations and phase diagrams of the phase-field crystal model with pinning. Physical Review E, 78(3), 1-7. . https://doi.org/10.1103/PhysRevE.78.031109