Boxed Plane Partitions as an Exactly Solvable Boson Model

Abstract

Plane partitions naturally appear in many problems of statistical physics and quantum field theory, for instance, in the theory of faceted crystals and of topological strings on Calabi-Yau threefolds. In this paper a connection is made between the exactly solvable model with the boson dynamical variables and a problem of enumeration of boxed plane partitions - three dimensional Young diagrams placed into a box of a finite size. The correlation functions of the boson model may be considered as the generating functionals of the Young diagrams with the fixed heights of its certain columns. The evaluation of the correlation functions is based on the Yang-Baxter algebra. The analytical answers are obtained in terms of determinants and they can also be expressed through the Schur functions.

21 pages, 9 figures

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