Histogram Monte Carlo Approach to Scaling Functions and Order Parameters of Phase Transition Models

Ralf K. Heilmann, A. M. Ferrenberg, D. P. Landau +1 more

Chin‐Kun Hu

Based on the subgraph expansions for phase transition models, we present a histogram Monte Carlo method to calculate the free energy and other physical quantities for such models as continuous functions of the system parameter. The method does not have any critical slowing down. We then use physical quantities thus obtained in a percolation renormalization group method to calculate critical point, critical exponents, and thermodynamic order parameter. Our method gives quite accurate results and may be applied to many phase transition models.

Akai Kurbanovich Murtazaev, Zhavrail G. Ibaev

Abstract Monte Carlo methods are used to study the anisotropic Ising model with competing interactions in the region of the phase transition from the modulated to the paramagnetic phase. Using histogram analysis of Monte Carlo data and the theory of finite-size scaling, it is shown that the transition from the modulated state to the paramagnetic one is a second-order phase transition. The critical parameters and temperatures of phase transitions in this region are calculated. It is shown that the modulated–paramagnetic phase transition cannot be described within the framework of the known universality classes of critical behavior.

Kurt Binder

Kurt Binder, Erik Luijten, Marcus Müller +2 more

Murtazaev Akai Kurbanovich, Ibaev Zhavrail Gadzhievich

The anisotropic Ising model with competing interactions in the region of transition from a modulated phase into paramagnetic state is investigated by the Monte-Carlo methods. By means of histogram analysis and the finite-size scaling method, the modulated – paramagnetic phase transition is shown to be a second order phase transition. Critical parameters and temperatures of phase transitions in this region are calculated.