A manifold of pure Gibbs states of the Ising model on the Lobachevsky plane

Abstract

In this paper we construct many `new' Gibbs states of the Ising model on the Lobachevsky plane, the millefeuilles. Unlike the usual states on the integer lattices, our foliated states have infinitely many interfaces. The interfaces are rigid and fill the Lobachevsky plane with positive density.

25 pages, 7 figures

References in corpus (1)

• A manifold of pure Gibbs states of the Ising model on a Cayley tree

Cited by in corpus (3)

• Extremal inhomogeneous Gibbs states for SOS-models and finite-spin models on trees
• Constraint percolation on hyperbolic lattices
• Counting Contours on Trees