Coordination number, Bethe lattice and random field Ising model

Abstract

The random field Ising model is studied on a Bethe lattice with coordination number q. An exact recursion relation for the local magnetisation due to the outer shells is calculated for a random field distribution equal to the sum of two delta functions. From the analysis of a fixed point of this relation, it is found that long-range order exists for q>2 as in the pure case. A tricritical point is obtained. Comparison of the location of the tricritical point at q=3 and at the mean field limit shows an overestimate of the mean field limit of 1/3 for the field and 1/8 for the temperature.