The Wavelet-Analysis at Monte–Carlo Modeling of Phase Transitions in a Ferroelastic Crystal of Lithium Ammonium Sulphate

Abstract

Using methods of the wavelet—analysis at Monte—Carlo modeling a behavior of thermodynamic parameters of Ising model for the ferroelectric—ferroelastic crystal of lithium ammonium sulphate LiNH₄SO₄ is studied. The discussed method is similar to Monte—Carlo Renormalization Group (MCRG), but it is more effective, thanks to a presence of algorithm of fast wavelet–transformation (WT). The short review of the wavelet transform and Monte—Carlo modeling by means of MCRG algorithm has been made. Temperature dependences of a specific heat capacity and dielectric permittivity for a set of lattice models with the sizes N × N at N = 64, 128, and 256 were derived as a result of 1, 2, 3-level WT. Critical exponents are found by numerical differentiation of a temperature dependence of thermodynamic parameters near a temperature of phase transition.

Keywords:

• Lithium ammonium sulfate
• ferroelectrics
• ferroelastics
• wavelet analysis
• Monte–Carlo modeling
• phase transition