Phase transitions and size effects in the Ising dipolar magnet

We consider a uniaxial dipolar magnet in a simple geometry (infinite slab of thickness D). For small D, a commonly observed structure is the stripe structure. For larger D, branching occurs in the domain pattern. The number of ramifications increases very slowly with D. The phase diagram of these magnetic structures is studied in the (H, T) plane. Finally, we show how the surface of the very ramified case (D → oo) has the same type of critical fluctuations as the (bulk) SK model of a spin glass (constant susceptibility at all temperatures below the transition).