Trimodal random-field Ising model on a Bethe lattice and the tricritical point.

Abstract

The random-field Ising model on a Bethe lattice is studied for a trimodal distribution P(${H}_{i}$)=p\ensuremath{\delta}(${H}_{i}$)+(1/2)(1-p) [\ensuremath{\delta}(${H}_{i}$-H)+\ensuremath{\delta}(${H}_{i}$ +H)]. The existence of a tricritical point as a function of p is analyzed, and it is observed that with coordination number q=3 for p=(1/3, which can be considered as a good approximation to a Gaussian distribution, there is a tricritical point in the phase diagram, in accordance with some recent series-expansion results on a three-dimensional Ising model where, even for a Gaussian distribution, a tricritical point was observed. Appropriate mean-field limits are recovered for q\ensuremath{\rightarrow}\ensuremath{\infty}. .AE