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32 Painlevé TranscendentsApplications

§32.16 Physical Applications

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Keywords:
Painlevé property, Painlevé transcendents, applications, continuous dynamical systems and mappings
Referenced by:
Erratum (V1.0.17) for Section 32.16, Erratum (V1.0.17) for References
Permalink:
http://dlmf.nist.gov/32.16
Clarification (effective with 1.0.17):
The references Wu et al. (1976) and McCoy et al. (1977) were inserted in Paragraph Other Applications for the Ising model. Incidentally, the editors have also corrected the title: to Physical Applications from Physical.

Suggested by Craig Tracy

See also:
Annotations for Ch.32

Statistical Physics

Statistical physics, especially classical and quantum spin models, has proved to be a major area for research problems in the modern theory of Painlevé transcendents. For a survey see McCoy (1992). See also McCoy et al. (1977), Jimbo et al. (1980), Essler et al. (1996), and Kanzieper (2002).

Integrable Continuous Dynamical Systems

See Bountis et al. (1982) and Grammaticos et al. (1991).

Other Applications

For the Ising model see Barouch et al. (1973), Wu et al. (1976), and McCoy et al. (1977).

For applications in 2D quantum gravity and related aspects of the enumerative topology see Di Francesco et al. (1995). For applications in string theory see Seiberg and Shih (2005).

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