caa a22 4500 467892423 CHVBK 20180406152752.0 cr unu---uuuuu 170328e20060301xx s 000 0 eng 10.1007/s10955-005-8031-9 doi (NATIONALLICENCE)springer-10.1007/s10955-005-8031-9 On the Mean-Field Spherical Model [Elektronische Daten] [Michael Kastner, Oliver Schnetz] 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. Springer Science + Business Media, Inc., 2006 Phase transitions nationallicence Spherical model nationallicence Microcanonical nationallicence Canonical nationallicence Ensemble nonequivalence nationallicence Partial equivalence nationallicence Fisher zeros of the partition function nationallicence ℝℙ N −1 σ-model nationallicence Mixed isovector/isotensor σ-model nationallicence Model equivalence nationallicence Topological approach nationallicence Kastner Michael Physikalisches Institut, Lehrstuhl für Theoretische Physik I, Universität Bayreuth, 95440, Bayreuth, Germany aut Schnetz Oliver Institut für Theoretische Physik III, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058, Erlangen, Germany aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1195-1214 0022-4715 122:6<1195 2006 122 10955 https://doi.org/10.1007/s10955-005-8031-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8031-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kastner Michael Physikalisches Institut, Lehrstuhl für Theoretische Physik I, Universität Bayreuth, 95440, Bayreuth, Germany aut NATIONALLICENCE 700 1- Schnetz Oliver Institut für Theoretische Physik III, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058, Erlangen, Germany aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1195-1214 0022-4715 122:6<1195 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer