Geodesic
Integrable models and combinatorics
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 5, pp. 789-856

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Relations between quantum integrable models solvable by the quantum inverse scattering method and some aspects of enumerative combinatorics and partition theory are discussed. The main example is the Heisenberg $XXZ$ spin chain in the limit cases of zero or infinite anisotropy. Form factors and some thermal correlation functions are calculated, and it is shown that the resulting form factors in a special $q$-parametrization are the generating functions for plane partitions and self-avoiding lattice paths. The asymptotic behaviour of the correlation functions is studied in the case of a large number of sites and a moderately large number of spin excitations. For sufficiently low temperature a relation is established between the correlation functions and the theory of matrix integrals. Bibliography: 125 titles.
Keywords: correlation functions, Heisenberg magnet, four-vertex model, generating functions, symmetric functions.
Mots-clés : plane partitions 
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N. M. Bogolyubov; K. L. Malyshev. Integrable models and combinatorics. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 5, pp. 789-856. http://geodesic.mathdoc.fr/item/RM_2015_70_5_a0/