P. Holicky, M. Zahradnik
Stratified Low Temperature Phases of Stratified Spin Models.
A general Pirogov Sinai Approach.
(225K, AmsTeX)
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.