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Mixing properties and exponential decay for lattice systems in finite volumes
 ANNALS OF PROBABILITY
, 2004
"... An infinitevolume mixing or exponentialdecay property in a spin system or percolation model reflects the inability of the influence of the conguration in one region to propagate to distant regions, but in some circumstances where such properties hold, propagation can nonetheless occur in finite v ..."
Abstract

Cited by 15 (1 self)
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An infinitevolume mixing or exponentialdecay property in a spin system or percolation model reflects the inability of the influence of the conguration in one region to propagate to distant regions, but in some circumstances where such properties hold, propagation can nonetheless occur in finite volumes endowed with boundary conditions. We establish the absense of such propagation, particularly in two dimensions in finite volumes which are simply connected, under a variety of conditions, mainly for the Potts model and the FortuinKasteleyn (FK) random cluster model, allowing external fields. For example, for the FK model in two dimensions we show that exponential decay of connectivity in infinite volume implies exponential decay in simply connected finite volumes, uniformly over all such volumes and all boundary conditions, and implies a strong mixing property for such volumes with certain types of boundary conditions. For the Potts model in two dimensions we show that exponential decay of correlations in infinite volume implies a strong mixing property in simply connected finite volumes, which includes exponential decay of correlations in simply connected finite volumes, uniformly over all such volumes and all boundary conditions.
SURFACE TENSION AND WULFF SHAPE FOR A LATTICE MODEL WITHOUT SPIN FLIP SYMMETRY
"... Abstract. We propose a new denition of surface tension and check it in a spin model of the PirogovSinai class without symmetry. We study the model at low temperatures on the phase transitions line and prove: (i) existence of the surface tension in the thermodynamic limit, for any orientation of th ..."
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Abstract. We propose a new denition of surface tension and check it in a spin model of the PirogovSinai class without symmetry. We study the model at low temperatures on the phase transitions line and prove: (i) existence of the surface tension in the thermodynamic limit, for any orientation of the surface and in all dimensions d 2; (ii) the Wul shape constructed with such a surface tension coincides with the equilibrium shape of the cluster which appears when xing the total spin magnetization (Wul problem). 1.