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statistical mechanics


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1: 26.20 Physical Applications
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). …
2: 17.17 Physical Applications
§17.17 Physical Applications
In exactly solved models in statistical mechanics (Baxter (1981, 1982)) the methods and identities of §17.12 play a substantial role. …
3: 8.24 Physical Applications
§8.24(ii) Incomplete Beta Functions
The function I x ( a , b ) appears in: Monte Carlo sampling in statistical mechanics (Kofke (2004)); analysis of packings of soft or granular objects (Prellberg and Owczarek (1995)); growth formulas in cosmology (Hamilton (2001)). …
4: 20.12 Mathematical Applications
This ability to uniformize multiply-connected spaces (manifolds), or multi-sheeted functions of a complex variable (Riemann (1899), Rauch and Lebowitz (1973), Siegel (1988)) has led to applications in string theory (Green et al. (1988a, b), Krichever and Novikov (1989)), and also in statistical mechanics (Baxter (1982)).
5: 5.20 Physical Applications
Solvable Models of Statistical Mechanics
6: 31.17 Physical Applications
§31.17(ii) Other Applications
Heun functions appear in the theory of black holes (Kerr (1963), Teukolsky (1972), Chandrasekhar (1984), Suzuki et al. (1998), Kalnins et al. (2000)), lattice systems in statistical mechanics (Joyce (1973, 1994)), dislocation theory (Lay and Slavyanov (1999)), and solution of the Schrödinger equation of quantum mechanics (Bay et al. (1997), Tolstikhin and Matsuzawa (2001), and Hall et al. (2010)). …
7: 23.21 Physical Applications
§23.21 Physical Applications
  • Statistical mechanics. See Baxter (1982, p. 434) and Itzykson and Drouffe (1989, §9.3).

  • 8: 22.18 Mathematical Applications
    See Baxter (1982, p. 471) for an example from statistical mechanics. … …
    9: Bibliography B
  • R. J. Baxter (1982) Exactly Solved Models in Statistical Mechanics. Academic Press Inc., London-New York.
  • 10: Bibliography S
  • I. Shavitt (1963) The Gaussian Function in Calculations of Statistical Mechanics and Quantum Mechanics. In Methods in Computational Physics: Advances in Research and Applications, B. Alder, S. Fernbach, and M. Rotenberg (Eds.), Vol. 2, pp. 1–45.