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

Daniel Gandolfo (1) , Jean Ruiz (1) , Senya Shlosman (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 IITP RAS - Inst. of the Information Transmission Problems

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.

Mots clés: geodesical family; Ising model; cross-ratio; interface; rigidity

Domaines: Physique mathématique [math-ph]

Daniel Gandolfo, Jean Ruiz, Senya Shlosman. A manifold of pure Gibbs states of the Ising model on the Lobachevsky plane. Communications in Mathematical Physics, 2015, 334 (1), pp.313-330. ⟨10.1007/s00220-014-2136-4⟩. ⟨hal-00875942⟩