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Revisiting the combinatorics of the 2D Ising model. (English) Zbl 1380.82017
The combinatorial method constitutes an important approach for the study of classical Ising models. The present paper provides short proofs of several combinatorial formulas (such as the Kac-Ward formula), which are useful in evaluating the partition function, multi-point fermionic observables, and spin and energy density correlations for the planar Ising model. A self-contained overview of the connections between several formalisms (dimer representation, Grassmann variables, disorder insertions, and combinatorial s-holomorphic observables) in the study of the planar Ising model is given. In the last section, the authors also make an attempt to generalize their results to the double-Ising model, which describes two identical planar Ising models with couplings at the boundary.

MSC:
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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