Year: 2012
Type: preprint
Abstract: 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 to some specific cases. Namely, first we study, in the case of a particular graph (the 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).
Source: arXiv (Cornell University)
Authors: Gandolfo, D., Rozikov, U. A., Ruiz, J.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1820965977