A Manifold of Pure Gibbs States of the Ising Model on the Lobachevsky Plane

2013/10/22 by Daniel Gandolfo, Jean Ruiz, Senya Shlosman · 1 citation
Mathematics · Physics and Astronomy · #Construct (python library) #Integer (computer science) #Ising model #Ising spin #Manifold (fluid mechanics) #Plane (geometry) #Random Matrices and Applications #Square-lattice Ising model #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP

paper · pdf · doi:10.1007/s00220-014-2136-4

25 pages, 7 figures

arxiv created 2013/10/22 · openalex publication_date 2014/08/14 · arxiv updated 2015/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Cited by

• Extremal Ising Gibbs States on Lobachevsky lattices

Related

• A manifold of pure Gibbs states of the Ising model on a Cayley tree
• Extremal Ising Gibbs States on Lobachevsky lattices
• Gibbs Measures for Long-Range Ising Models
• Interfaces and droplets in quantum lattice models
• Rigidity of interfaces in the Falicov-Kimball model