Thursday, October 25, 2012

1210.6586 (D. Gandolfo et al.)

On four state Hard Core Models on the Cayley Tree    [PDF]

D. Gandolfo, U. A. Rozikov, J. Ruiz
We consider a nearest-neighbor four state hard-core (HC) model on the homogeneous Cayley tree of order $k$. The Hamiltonian of the model is considered on a set of "admissible" configurations. Admissibility is specified through a graph with four vertices. We first exhibit conditions (on the graph and on the parameters) under which the model has a unique Gibbs measure. Next we turn on some specific cases. Namely, first we study, in case of particular graph (diamond), translation-invariant and periodic Gibbs measures. We provide in both cases the equations of the transition lines separating uniqueness from non--uniqueness regimes. Finally the same is done for "fertile" graphs, the so--called stick, gun, and key (here only translation invariant states are taken into account).
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