Integrable structure of melting crystal model with two q-parameters

Integrable structure of melting crystal model with two q-parameters

This paper explores integrable structures of a generalized melting crystal model that has two q-parameters q1, q2. 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 p...

Integrable structure of modified melting crystal model

Our previous work on a hidden integrable structure of the melting crystal model (the U(1) Nekrasov function) is extended to a modified crystal model. As in the previous case, “shift symmetries” of a quantum torus algebra plays a central role. With the aid of these algebraic relations, the partition function of the modified model is shown to be a tau function of the 2D Toda hierarchy. We conject...

Integrable structure of melting crystal models

Melting of 2D liquid crystal colloidal structure

Using video microscopy, we investigated melting of a two-dimensional colloidal system, formed by glycerol droplets at the free surface of a nematic liquid crystalline layer. Analyzing different structure correlation functions, we conclude that melting occurs through an intermediate hexatic phase, as predicted by the KosterlitzThouless-Halperin-Nelson-Young(KTHNY) theory. However, the temperatur...

Two-dimensional melting of a crystal of ferrofluid spikes.

We report the observation of the transition from an ordered solidlike phase to a disordered liquidlike phase of a lattice of spikes on a ferrofluid surface submitted to horizontal sinusoidal vibrations. The melting transition occurs for a critical spike displacement which is experimentally found to follow the Lindemann criterion, for two different lattice topologies (hexagonal and square) and o...