96-301 P. Holicky, M. Zahradnik

Stratified Low Temperature Phases of Stratified Spin Models. A general Pirogov Sinai Approach. (225K, AmsTeX) Jun 17, 96

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Abstract. We adapt and improve the existing Pirogov -- Sinai technology to obtain a general and unifying approach to the study of low temperature, ``stratified'' phases for classical spin models whose hamiltonian may not even be translation invariant but is ``stratified'' i.e. invariant with respect to all ``horizontal'' shifts (not changing the last coordinate). Examples are ``stratified'' versions of classical models like the Ising model with ``vertically dependent'' external field; models in halfspaces or layers and also those translation invariant models where Dobrushin's phases with rigid interfaces (one or more) appear. Our method brings some clarification and sharpening even when applied to the ordinary situations of the Pirogov -- Sinai theory ([S],[Z]). Our main result transcripts the question of characterizing the ``stratified'' Gibbs states of the given model to the question of finding the {\it ground states} of some auxiliary {\it one dimensional\/} model with infinite range but quickly decaying interactions.

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