Modified melting crystal model and Ablowitz-Ladik hierarchy

Abstract

This is a review of recent results on the integrable structure of the ordinary and modified melting crystal models. When deformed by special external potentials, the partition function of the ordinary melting crystal model is known to become essentially a tau function of the 1D Toda hierarchy. In the same sense, the modified model turns out to be related to the Ablowitz-Ladik hierarchy. These facts are explained with the aid of a free fermion system, fermionic expressions of the partition functions, algebraic relations among fermion bilinears and vertex operators, and infinite matrix representations of those operators.

10 pages, 4 figures, contribution to proceedings of the conference "Physics and Mathematic of Nonlinear Phenomena", Gallipoli, Italy, June 23-28, 2013

References in corpus (2)

• Melting Crystal, Quantum Torus and Toda Hierarchy
• Integrable structure of modified melting crystal model

Cited by in corpus (5)

• Open string amplitudes of closed topological vertex
• Orbifold melting crystal models and reductions of Toda hierarchy
• Generalized Ablowitz-Ladik hierarchy in topological string theory
• Cubic Hodge integrals and integrable hierarchies of Volterra type
• 4D limit of melting crystal model and its integrable structure