Leplaideur, Renaud, and Watbled, Frédérique (2020) Curie–Weiss type models for general spin spaces and quadratic pressure in ergodic theory. Journal of Statistical Physics, 181 (1). pp. 263-292.

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Abstract

We extend results on quadratic pressure and convergence of Gibbs measures from Leplaideur and Watbled (Bull Soc Math France 147(2):197–219, 2019) to some general models for spin spaces. We define the notion of equilibrium state for the quadratic pressure and show that under some conditions on the maxima for some auxiliary function, the Gibbs measure converges to a convex combination of eigen-measures for the Transfer Operator. This extension works for dynamical systems defined by infinite-to-one maps. As an example, we compute the equilibrium for the mean-field XY model as the number of particles goes to + ∞.

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