Multiphase structure of finite‐temperature phase diagram of the Blume–Capel model. Wang–Landau sampling method

Abstract

We investigate the density of states (DOS) in an antiferromagnetic spin-system on a square lattice described by the Blume-Capel (BC) model. We use a new and very efficient simulation method, proposed by Wang and Landau, in which we estimate very precisely DOS by sampling in the space of energy. Then we calculate the thermodynamical averages like internal energy, free energy, specific heat and entropy.The BC model exhibits multicritical behaviour such as first-or second-order transitions and tricritical points. It is known that the ground state of the model can exhibit two kinds of staggered antiferromagnetic phases: AF 1 (two interpenetrating lattices with S = -1 and S = 1) and AF 2 (S = -1 and S = 0 for H < 0; S = 1 and S = 0 for H > 0). We analyze the coexistence of such phases at finite temperatures and determine border lines between them. To understand the microscopic nature of such boundaries we present also some results obtained with the standard Monte Carlo method.

Phase behaviour and structure of a superionic liquid in nonpolarized nanoconfinement

“…The phase diagram, location of the tricritical point, as well as values of the critical exponents were quantitatively analysed within high- [93][94][95] , and low-temperature series expansion methods 95 , different effective theories [96][97][98] , variational approximations 99 , mean-field renormalization group (RG) 100 , Kadanoffs lower-bound RG transformations 101 , nonperturbative RG schemes 102 , various Monte-Carlo methods [103][104][105][106][107][108][109][110][111][112] , constant-coupling approximation 113 , transfer matrix finite-size scaling 114 , lowest approximation of cluster variation method 115 , and pair approximations for the free energy 110 .…”

“…We note that already a mean-field analysis presented in the seminal works [87,88] showed that the BC spin-1 model exhibits a second-order phase transition line separating a disordered phase from an ordered one, and changing at a tricritical point into the line of the first-order phase trans itions for sufficiently large values of ∆. The phase diagram, location of the tricritical point, as well as values of the critical exponents were quantitatively analysed within high- [92][93][94], and lowtemperature series expansion methods [94], different effective theories [95][96][97], variational approx imations [98], mean-field renormalization group (RG) [99], Kadanoffs lower-bound RG transformations [100], nonperturbative RG schemes [101], various Monte-Carlo methods [102][103][104][105][106][107][108][109][110][111], constant-coupling approximation [112], transfer matrix finite-size scaling [113], lowest approximation of cluster variation method [114], and pair approximations for the free energy [109].…”

Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior

“…( 1) can be mapped onto the classical spin-1 Blume-Capel (BC) model. The BC model has been studied by cluster-variation [37] and Bethelattice approaches [36] and by Monte Carlo simulations [38][39][40][41][42]. Based on these results, we expect rich phase behavior, involving direct and re-entrant symmetry-breaking phase transitions between 'ordered' and 'disordered' phases.…”

“…We solve this model exactly on a Bethe lattice [34] with coordination number q, which approximate lattices with the same coordination number (it can also be seen as an approximation to off-lattice systems with, on average, q neighbors) [35]. This model can be mapped onto the well known antiferromagnetic Blume-Capel model, which has been treated by the Bethe-lattice approach [36], cluster-variation method [37] and simulations [38][39][40][41][42] in the context of magnetic systems.…”

The effective‐site percolation approach in two dimensions

“…Let me present at the end an exemplary analysis for spin and electron models (for more detailed analyses see our recent papers [22,23] …”