Continuous symmetry breaking in a mean-field model

T Eisele, R S Ellis
1983 Journal of Physics A: Mathematical and General  
A magnetic system on the sites { j / n ; j = 1, . . . , n } of the circle T = R (mod 1) is studied in the limit n + 03. The interaction is defined in terms of a continuous function J ( x , y), x , y E T. For any ferromagnetic J ( J >O) which satisfies a normalisation condition, the thermodynamic behaviour is identical to that of the Curie-Weiss model ( J = 1). This simple case is in contrast to the behaviour for a class of translation invariant, nonferromagnetic J, for which a continuum of
more » ... a continuum of equilibrium states exists for sufficiently low temperatures. In both cases a probabilistic interpretation of the equilibrium states is given.
doi:10.1088/0305-4470/16/1/026 fatcat:fsztdcpamfes3ecqqlz2ksiaay