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SUMMARY:Discrete holomorphicity and Ising model transfer matrix formalism 
 - Kalle Kytölä  (Helsinki)
DTSTART:20130226T163000Z
DTEND:20130226T173000Z
UID:TALK43330@talks.cam.ac.uk
CONTACT:12974
DESCRIPTION:The transfer matrix formalism is a classical approach to the t
 wo-dimensional Ising model\, and some of the most remarkable exact calcula
 tions about the model were obtained using this approach. Discrete holomorp
 hicity\, on the other hand\, has recently lead to proofs of conformal inva
 riance of energy and spin correlations in the scaling limit of the model t
 aken at the critical point\, and to convergence results of interfaces to S
 chramm-Loewner evolutions. In this talk we consider relations of discrete 
 holomorphicity and transfer matrix formalism. In particular it will be sho
 wn that the transfer matrix can be reconstructed from discrete analytic co
 ntinuation of s-holomorphic (or massive s-holomorphic) functions\, and tha
 t fermion operators in the transfer matrix formalism are operator valued (
 massive) s-holomorphic functions. Finally we discuss rudiments of a fermio
 nic conformal field theory description of the scaling limit of the Ising m
 odel based on these results.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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