Microcanonical Determination of the Interface Tension of Flat and Curved Interfaces from Monte Carlo Simulations

Abstract

The investigation of phase coexistence in systems with multi-component order parameters in finite systems is discussed, and as a generic example, Monte Carlo simulations of the two-dimensional q-state Potts model (q=30) on LxL square lattices (40<=L<=100) are presented. It is shown that the microcanonical ensemble is well-suited both to find the precise location of the first order phase transition and to obtain an accurate estimate for the interfacial free energy between coexisting ordered and disordered phases. For this purpose, a microcanonical version of the heatbath algorithm is implemented. The finite size behaviour of the loop in the curve describing the inverse temperature versus energy density is discussed, emphasizing that the extrema do not have the meaning of van der Waals-like "spinodal points" separating metastable from unstable states, but rather describe the onset of heterophase states: droplet/bubble evaporation/condensation transitions. Thus all parts of these loops, including the parts that correspond to a negative specific heat, describe phase coexistence in full thermal equilibrium. However, the estimates for the curvature-dependent interface tension of the droplets and bubbles suffer from unexpected and unexplained large finite size effects which need further study.

submitted to special issue "Liquid Matter" of Journal of Physics C: Condensed Matter on occasion of the 8th Liquid Matter Conference held Sept. 6-10, 2011 in Vienna, Austria

References in corpus (5)

• Curvature Dependence of Surface Free Energy of Liquid Drops and Bubbles: A Simulation Study
• Monte Carlo Test of the Classical Theory for Heterogeneous Nucleation Barriers
• Microcanonical Approach to the Simulation of First-Order Phase Transitions
• Optimized broad-histogram simulations for strong first-order phase transitions: Droplet transitions in the large-Q Potts model
• Generalized-ensemble simulations and cluster algorithms

Cited by in corpus (5)

• Dynamic off-equilibrium transition in systems slowly driven across thermal first-order phase transitions
• Dynamic finite-size scaling at first-order transitions
• Anomalous finite-size scaling at thermal first-order transitions in systems with disordered boundary conditions
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models
• Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models