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Phase transition for classical fermions. (English. Russian original) Zbl 0930.60097
Math. Notes 63, No. 4, 560-562 (1998); translation from Mat. Zametki 63, No. 4, 635-637 (1998).
There is no commonly accepted notion of a classical analogue for quantum fermions. One recipe amounts to a formal limit in relevant formulas, like Hartree or Thomas-Fermi type equations. The main objective of the paper is to give lattice random variable model that mimics the behaviour expected from “classical fermions” and gives rise to formulas obtained in the semiclassical limit. Equilibrium distributions are utilized. It is found that a second-order phase transition is possible, corresponding to that from the superconductive to the normal state of matter.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B26 Phase transitions (general) in equilibrium statistical mechanics
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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References:
[1] V. P. Maslov,Russian J. Math. Phys.,5, No. 3, 405–410 (1997).
[2] V. P. Maslov,Mat. Zametki [Math. Notes],62, No. 4, 633–634 (1997).
[3] V. P. Maslov,Mat. Zametki [Math. Notes],63, No. 1, 145–146 (1998).
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