Boxed Plane Partitions as an Exactly Solvable Boson Model

TL;DR

This paper establishes an exactly solvable boson model linked to the enumeration of boxed plane partitions, providing analytical solutions via determinants and Schur functions, with applications in statistical physics and quantum field theory.

Contribution

It introduces a novel connection between a solvable boson model and the enumeration of three-dimensional Young diagrams within a finite box.

Findings

Correlation functions serve as generating functionals for fixed-height Young diagrams.

Analytical solutions are expressed through determinants and Schur functions.

The model's correlation functions are derived using the Yang-Baxter algebra.

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.