Dobrushin states for classical spin systems with complex interactions

Details Dobrushin states for classical spin systems with complex interactions Dobrushin states for classical spin systems with complex interactions

Dec 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997jsp....89..895b&link_type=abstract

Journal of Statistical Physics, Volume 89, Issue 5-6, pp. 895-928

Physics

2

Dobrushin States, Interfaces, Surface Tension, Pirogov, Sinai Theory, Complex Interactions

Scientific paper

We consider a classical spin system on the hypercubic lattice with a general interaction of the form H = β } {4}sumlimits_{begin{array/*{20c} {x,y:} \ {|x - y| = 1} \ } {|s_x - s_y | - h} sumlimits_x {x{}_x + } sumlimits_A {λ _A prodlimits_{y in A} {S_y } } are the spin variables, Β is the inverse temperature, h is the magnetic field, and λ A are translation-invariant coupling constants satisfying λ A = 0 if diam A > l. No symmetry relating the configurations s ={sinx} and-s= -s x is assumed. In dimension d-3, we construct low-temperature States which break the translation invariance of the system by introducing so-called Dobrushin boundary conditions which force a horizontal interface into the system. In contrast to previous constructions, our methods work equally well for complex interactions, and should therefore be generalizable to quantum spin systems.

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