A Manifold of Pure Gibbs States of the Ising Model on the Lobachevsky Plane
Copyright policy )A Manifold of Pure Gibbs States of the Ising Model on the Lobachevsky Plane
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
- French National Centre for Scientific Research France
- Centre national de la recherche scientifique France
- Centre de Physique Théorique France
- Russian Academy of Sciences Russian Federation
- Université de Toulon France
FOS: Physical sciences, Gibbs states, Cayley trees, Mathematical Physics (math-ph), [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], geodesical family, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, Trees, cross-ratio, rigidity, Ising model, interface, Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics, Mathematical Physics
FOS: Physical sciences, Gibbs states, Cayley trees, Mathematical Physics (math-ph), [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], geodesical family, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, Trees, cross-ratio, rigidity, Ising model, interface, Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics, Mathematical Physics
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