Discrete Holomorphicity and Ising Model Operator Formalism

We explore the connection between the transfer matrix formalism and discrete complex analysis approach to the two dimensional Ising model. We construct a discrete analytic continuation matrix, analyze its spectrum and establish a direct connection with the critical Ising transfer matrix. We show that the lattice fermion operators of the transfer matrix formalism satisfy, as operators, discrete holomorphicity, and we show that their correlation functions are Ising parafermionic observables. We extend these correspondences also to outside the critical point. We show that critical Ising correlations can be computed with operators on discrete Cauchy data spaces, which encode the geometry and operator insertions in a manner analogous to the quantum states in the transfer matrix formalism.

Published in:
To be published - 2014
Presented at:
Analysis, Complex Geometry, and Mathematical Physics : A Conference in Honor of Duong H. Phong, Columbia, NYC, USA, May 7-11, 2013

 Record created 2014-07-21, last modified 2019-08-12

Download fulltext

Rate this document:

Rate this document:
(Not yet reviewed)