Properties of the branched state of an Ising dipolar magnet

Abstract

We consider the thermodynamic properties of the branched state of an Ising dipolar magnet confined in a slab of thickness D. Within the framework of the Lifshitz and Privorotskii models (i) we derive, for large D, scaling laws for the period of the structure, the surface magnetization, and the number of branching, for zero external field H in the whole range 0 ≤ T ≤ T 0 (T0 is the Curie temperature of the branched structure) ; (ii) Using the results of a numerical study on the equilibrium configuration of the singly-branched system when H is present, we predict that increasing H at fixed D, T causes the multiply-branched system to undergo a series of first order transitions to lesser and lesser ramified states. A phase diagram for the critical curve DC(H) is given; (iii) The surface state of the quasi-infinitely branched state is shown to possess a constant susceptibility for all T ≤ T0