An English translation of Pólya (1937) on applications of combinatorics to chemistry has been published as Pólya and Read (1987). Other articles on this subject are de Bruijn (1981) and Rouvray (1995). The latter reference also describes chemical applications of other combinatorial techniques.
Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993). For an application of statistical mechanics to combinatorics, see Bressoud (1999).