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arXiv · 1303.3017

The fermionic observable in the Ising model and the inverse Kac-Ward operator

Marcin Lis
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Abstract

We show that the critical Kac-Ward operator on isoradial graphs acts in a certain sense as the operator of s-holomorphicity, and we identify the fermionic observable for the spin Ising model as the inverse of this operator. This result is partially a consequence of a more general observation that the inverse Kac-Ward operator for any planar graph is given by what we call a fermionic generating function. Furthermore, using bounds for the spectral radius and operator norm of the Kac-Ward transition matrix, we provide a general picture of the non-backtracking walk representation of the critical and supercritical inverse Kac-Ward operators on isoradial graphs.

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Marcin Lis. 2015-04-30. The fermionic observable in the Ising model and the inverse Kac-Ward operator. https://doi.org/10.1007/s00023-013-0295-z

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