Discrete Holomorphicity in Solvable Lattice Models

Robert Weston (Heriot-Watt University)

Tuesday 21st April, 2015 15:00-16:00 Maths 416


I will introduce the concept of discrete holomorphicity for functions on a 2D lattice embedded into the complex plane. I will briefly discuss the important role that functions with this property have played in proving the existence and uniqueness of the continuum limit of certain models of statistical mechanics. I will then go on to discuss a systematic procedure for constructing discretely  holomorphic operators in solvable statistical mechanical models in terms of the underlying quantum group symmetry of these models.  This procedure will be illustrated for loop models and the Chiral Potts model. I will finally show how the resulting discrete holomorphicity conditions for non-critical models leads directly to an identification of these models with a corresponding perturbed conformal field theory. 

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