Mean-Field Theory is Exact for the Random-Field Model with Long-Range Interactions

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.

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

Mean-field expansion for spin models with medium-range interactions

We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N)-invariant spin models with medium-range interactions. We perform a systematic expansion around the mean-field solution, obtaining the universal crossover curves and their leading corrections. In particular we show that, in three dimensions, the leading correction scales as R−3, R being the ra...

Exact Mean - Field Solutions of the Asymmetric Random Average Process 3 2 . A Functional Equation of Exact Mean - Field

We consider the asymmetric random average process (ARAP) with continuous mass variables and parallel discrete time dynamics studied recently by Krug/Garcia and Rajesh/Majumdar [both Jrl. Stat. Phys. 99 (2000)]. The model is defined by an arbitrary state-independent fraction density function φ(r) with support on the unit interval. We examine the exactness of mean-field steady-state mass distribu...

Maximum entropy principle explains quasistationary states in systems with long-range interactions: the example of the Hamiltonian mean-field model.

A generic feature of systems with long-range interactions is the presence of quasistationary states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian mean-field model, we demonstrate that a maximum entropy principle applied to the associated Vlasov equation explains known features of such states for a wide range of initial conditions. We are able to repro...