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 on any planar graph is given by what we call a fermionic generating function. We also present 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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Communicated by Denis Bernard.
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Lis, M. The Fermionic Observable in the Ising Model and the Inverse Kac–Ward Operator. Ann. Henri Poincaré 15, 1945–1965 (2014). https://doi.org/10.1007/s00023-013-0295-z
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DOI: https://doi.org/10.1007/s00023-013-0295-z