Boundary Conditions for Translation- Invariant Gibbs Measures of the Potts Model on Cayley Trees

Daniel Gandolfo (1, 2) , M. M. Rakhmatullaev (3) , U.A. Rozikov (3)

1 CPT - E5 Physique statistique et systèmes complexes
2 CPT - Centre de Physique Théorique - UMR 7332
3 Institute of Mathematics

We consider translation-invariant splitting Gibbs measures (TISGMs) for the q-state Potts model on a Cayley tree of order two. Recently a full description of the TISGMs was obtained, and it was shown in particular that at sufficiently low temperatures their number is 2q − 1. In this paper for each TISGM μ we explicitly give the set of boundary conditions such that limiting Gibbs measures with respect to these boundary conditions coincide with μ.

Mots clés: Cayley tree; Potts model; boundary condition; Gibbs measure

Domaines: Mécanique statistique [cond-mat.stat-mech]

Daniel Gandolfo, M. M. Rakhmatullaev, U.A. Rozikov. Boundary Conditions for Translation- Invariant Gibbs Measures of the Potts Model on Cayley Trees. Journal of Statistical Physics, 2017, 167 (5), pp.1164. ⟨10.1007/s10955-017-1771-5⟩. ⟨hal-01591298⟩