Random-field Blume-Capel model: Mean-field theory

Random-field Blume-Capel model: Mean-field theory.

Mixing times for the Mean-field Blume-capel Model via Aggregate Path Coupling

We investigate the relationship between the mixing times of the Glauber dynamics of a statistical mechanical system with its thermodynamic equilibrium structure. For this we consider the mean-field Blume-Capel model, one of the simplest statistical mechanical models that exhibits the following intricate phase transition structure: within a two dimensional parameter space there exists a curve at...

Weighted Mean Field Theory for the Random Field Ising Model

We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe critical behavior arising from the weighted sum. The resulting exponents are calculated.

Mean - Field Study of the Degenerate Blume - Emery - Griffiths Model in a Random Crystal Field

The degenerate Blume-Emery-Griffiths (DBEG) model has recently been introduced in the study of martensitic transformation problems. This model has the same Hamiltonian as the standard Blume-Emery-Griffiths (BEG) model but, to take into account vibrational effects on the martensitic transition, it is assumed that the states S = 0 have a degeneracy p (p = 1 corresponds to the usual BEG model). In...

Random-cluster representation of the Blume–Capel model

The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume–Capel model. It has three parameters, a vertex parameter a, an edge parameter p, and a cluster weighting factor q. Stochastic comparisons of measures are developed for the ‘vertex marginal’ when q ∈ [1, 2], and the ‘edge marginal’ when q ∈ [1,∞). Taken in conjunction with arguments used earl...