Microcanonical entropy of the spherical model with nearest-neighbour interactions

Details Microcanonical entropy of the spherical model with nearest-neighbour interactions Microcanonical entropy of the spherical model with nearest-neighbour interactions

2009-09-30

arxiv.org/abs/0909.5638v2

Journal of Statistical Mechanics: Theory and Experiment (2009) P12007

Physics

Condensed Matter

Statistical Mechanics

14 pages, 6 figures

Scientific paper

10.1088/1742-5468/2009/12/P12007

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.

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