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Название: On the Mean-Field Spherical Model
Авторы: Kastner M., Schnetz O.
Exact solutions are obtained for the mean-ﬁeld spherical model, with or without an external magnetic ﬁeld, for any ﬁnite or inﬁnite number N of degrees of freedom, both in the microcanonical and in the canonical ensemble. The canonical result allows for an exact discussion of the loci of the Fisher zeros of the canonical partition function. The microcanonical entropy is found to be nonanalytic for arbitrary ﬁnite N. The mean-ﬁeld spherical model of ﬁnite size N is shown to be equivalent to a mixed isovector/isotensor σ-model on a lattice of two sites. Partial equivalence of statistical ensembles is observed for the mean-ﬁeld spherical model in the thermodynamic limit. A discussion of the topology of certain state space submanifolds yields insights into the relation of these topological quantities to the thermodynamic behavior of the system in the presence of ensemble nonequivalence.