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).

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

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).