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Spin systems, statistical mechanics and Painlevé functions. (English) Zbl 0875.35080
Levi, Decio (ed.) et al., Painlevé transcendents: their asymptotics and physical applications. Proceedings of the NATO Advanced Research Workshop, Sainte-Adèle, Canada, September 3-7, 1990. New York, NY: Plenum Press. NATO ASI Ser., Ser. B, Phys. 278, 377-391 (1992).
Summary: We review the role of Painlevé functions in the theory of the Ising model and discuss the prospect of extending these results to the other solvable statistical mechanical models related to conformal field theory.
MSC:
35Q40PDEs in connection with quantum mechanics
82B20Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
81T25Quantum field theory on lattices