Free energies of theϕ4model from Wang-Landau simulations

Abstract

Using the Wang-Landau algorithm we derive the full thermal order parameter probability distribution of the ${\varphi }^4$ model for various displacive degrees and temperatures and calculate the resulting free energies. We obtain high-precision data on the shape of the free-energy barrier separating states of opposite order parameter values. For order-disorder-like systems, i.e., at low displacive degree we observe phase separation below the transition temperature. A model taking into account the surface free energy related to different domain shapes, which fits the simulation data extremely well at low temperatures, is constructed. The interpretation of the results in the context of Landau or Landau-Ginzburg theory is discussed and an improved setup for simulating Landau potentials is proposed.