- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:49
Annales de l’Institut Henri Poincaré D
Ann. Inst. Henri Poincaré Comb. Phys. Interact.
AIHPD
2308-5827
2308-5835
General
Combinatorics
Quantum theory
10.4171/AIHPD
http://www.ems-ph.org/doi/10.4171/AIHPD
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
2
2015
2
Kac–Ward operators, Kasteleyn operators, and s-holomorphicity on arbitrary surface graphs
David
Cimasoni
Université de Genève, GENÈVE 4, SWITZERLAND
Kac-Ward operator, Kasteleyn operator, s-holomorphic functions, Ising model
The conformal invariance and universality results of Chelkak-Smirnov on the two-dimensional Ising model hold for isoradial planar graphs with critical weights. Motivated by the problem of extending these results to a wider class of graphs, we de fine a generalized notion of s-holomorphicity for functions on arbitrary weighted surface graphs. We then give three criteria for s-holomorphicity involving the Kac–Ward, Kasteleyn, and discrete Dirac operators, respectively. Also, we show that some crucial results known to hold in the planar isoradial case extend to this general setting: in particular, spin-Ising fermionic observables are s-holomorphic, and it is possible to de fine a discrete version of the integral of the square of an s-holomorphic function. Along the way, we obtain a duality result for Kac–Ward determinants on arbitrary weighted surface graphs.
Statistical mechanics, structure of matter
Manifolds and cell complexes
113
168
10.4171/AIHPD/16
http://www.ems-ph.org/doi/10.4171/AIHPD/16