Microcanonical entropy of the spherical model with nearest-neighbour interactions

Abstract

For the spherical model with nearest-neighbour interactions, the microcanonical entropy s(e,m) is computed analytically in the thermodynamic limit for all accessible values of the energy e and the magnetization m per spin. The entropy function is found to be concave (albeit not strictly concave), implying that the microcanonical and the canonical ensembles are equivalent, despite the long-range nature of the spherical constraint the spins have to obey. Two transition lines are identified in the (e,m)-plane, separating a paramagnetic phase from a ferromagnetic and an antiferromagnetic one. The resulting microcanonical phase diagram is compared to the more familiar canonical one.

14 pages, 6 figures

References in corpus (7)

• An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
• Microcanonical Analyses of Peptide Aggregation Processes
• On the mean-field spherical model
• Phase Transitions from Saddles of the Potential Energy Landscape
• Nonanalyticities of the entropy induced by saddle points of the potential energy landscape
• Microcanonical phase diagrams of short-range ferromagnets
• Topological approach to phase transitions and inequivalence of statistical ensembles

Cited by in corpus (4)

• Nonequivalence of ensembles in the Curie-Weiss anisotropic quantum Heisenberg model
• On the thermodynamics of classical micro-canonical systems
• Microcanonical analysis of the Curie-Weiss anisotropic quantum Heisenberg model in a magnetic field
• Ensemble equivalence in spin systems with short-range interactions