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We discuss a Curie-Weiss model with two groups in the critical regime. This is the region where the central limit theorem does not hold any more but the mean magnetization still goes to zero as the number of spins grows. We show that the total magnetization normalized by N 3/4 converges to a non-trivial distribution which is not Gaussian, just as in the single-group Curie-Weiss model.

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We analyse a Curie-Weiss model with two disjoint groups of spins with homogeneous coupling. We show that similarly to the single-group Curie-Weiss model a bivariate law of large numbers holds for the normed sums of both groups’ spin variables. We also show central limit theorem in the high temperature regime.