Spring 2016

A Complexity Classification of Six Vertex Models as Holant Problems

Tuesday, Jun. 6, 2017 9:30 am10:30 am

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I will give a dichotomy theorem for all complex valued six vertex models expressed as Holant problems with an (asymmetric) constraint function of arity 4. We also describe a refined classification that show that there is an additional tractable class of problems for planar instances. There is a (non-local) connection between this and spin systems, where the spin values are represented by orientations of loops. Time permitting, I will also describe an extension to the 8-vertex model.  These will be basic building blocks for a full classification theorem on Holant problems on the Boolean domain for all constraint functions that are not necessarily symmetric.
Joint work with Zhiguo Fu, Shuai Shao and Mingji Xia