# Statistical mechanics of lattice models

The study of exactly solved (integrable) lattice models in statistical mechanics is an area in which Australia has a leading international reputation. The knowledge and understanding obtained from exactly solved models has greatly enhanced progress in the theory of phase transitions and critical phenomena.

The most significant results achieved to date have been for two-dimensional lattice models and one-dimensional quantum systems. In many cases the exact results obtained provide important testbeds for the myriad ideas and computational methods of modern theoretical physics. Integrable models are also of direct relevance to -- and in some cases the driving force behind -- formerly unrelated areas of mathematics and/or physics, such as the study of knots, links and braids,
quantum groups, combinatorics and conformal field theory. Integrable models are also playing a central role in the AdS/CFT correspondence in mathematical physics which conjectures an equivalence between theories of gravity on a curved space and gauge theories defined on their boundary.

Integrable models have also been realised directly in experiments, most recently with the trapping and cooling of quantum gases in tightly confined optical wave guides.

Our current work is on understanding the implications of a remarkable connection between the theory of Yang-Baxter integrability for lattice models and the notion of discrete holomorphicity applied to a parafermionic observable on the lattice.

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