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Absence of symmetry breaking for systems of rotors with random interactions

Authors:	Cezar A Bonato Massimo Campanino

Institution:	(1) Departamento de Fisica, Universidade Federal da Paraiba, João Pessosa, Pb, Brazil;(2) Istituto di Matematica, Universita' della Basilicata, Potenza, Italy

Abstract:	We prove that Gibbs states for the Hamiltonian $H = - \sum\nolimits_{xy} {\tilde J_{xy} s_x \cdot s_y }$ , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if $\tilde J_{xy} = {{J_{xy} } \mathord{\left/ {\vphantom {{J_{xy} } {\left\| {x - y} \right\|^\alpha }}} \right. \kern-\nulldelimiterspace} {\left\| {x - y} \right\|^\alpha }}$ withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.

Keywords:	Disordered systems Gibbs states symmetry breaking
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