Integrable structure of melting crystal model with two q-parameters

Understand

This paper explores integrable structures of a generalized melting crystal model that has two $q$-parameters $q_1,q_2$.

• This model, like the ordinary one with a single $q$-parameter, is formulated as a model of random plane partitions (or, equivalently, random 3D Young diagrams).
• The Boltzmann weight contains an infinite number of external potentials that depend on the shape of the diagonal slice of plane partitions.
• The partition function is thereby a function of an infinite number of coupling constants $t_1,t_2,...$ and an extra one $Q$.