Modified melting crystal model and Ablowitz-Ladik hierarchy

Physics and Mathematics of Nonlinear Phenomena 2013

Takasaki, Kanehisa^1

Human and Environmental Studies, Kyoto University, Kyoto 606-8501, Japan^1

关键词: Algebraic relations;    External potential;    Fermion systems;    Matrix representation;    Modified model;    Partition functions;    Toda hierarchy;    Vertex operators;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012041/pdf
DOI  :  10.1088/1742-6596/482/1/012041

来源: IOP

【 摘 要 】

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.