Kac–Ward operators, Kasteleyn operators, and s-holomorphicity on arbitrary surface graphs
Annales de l’Institut Henri Poincaré D, Tome 2 (2015) no. 2, pp. 113-168.

�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.

Publié le :
DOI : 10.4171/aihpd/16
Classification : 82-XX, 57-XX
Mots-clés : Kac-Ward operator, Kasteleyn operator, s-holomorphic functions, Ising model 
@article{AIHPD_2015__2_2_113_0,
     author = {Cimasoni, David},
     title = {Kac{\textendash}Ward operators, {Kasteleyn} operators, and $s$-holomorphicity on arbitrary surface graphs},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {113--168},
     publisher = {EMS Press},
     volume = {2},
     number = {2},
     year = {2015},
     doi = {10.4171/aihpd/16},
     zbl = {1334.82008},
     language = {en},
     url = {https://www.numdam.org/articles/10.4171/aihpd/16/}
}
TY  - JOUR
AU  - Cimasoni, David
TI  - Kac–Ward operators, Kasteleyn operators, and $s$-holomorphicity on arbitrary surface graphs
JO  - Annales de l’Institut Henri Poincaré D
PY  - 2015
SP  - 113
EP  - 168
VL  - 2
IS  - 2
PB  - EMS Press
UR  - https://www.numdam.org/articles/10.4171/aihpd/16/
DO  - 10.4171/aihpd/16
LA  - en
ID  - AIHPD_2015__2_2_113_0
ER  - 
%0 Journal Article
%A Cimasoni, David
%T Kac–Ward operators, Kasteleyn operators, and $s$-holomorphicity on arbitrary surface graphs
%J Annales de l’Institut Henri Poincaré D
%D 2015
%P 113-168
%V 2
%N 2
%I EMS Press
%U https://www.numdam.org/articles/10.4171/aihpd/16/
%R 10.4171/aihpd/16
%G en
%F AIHPD_2015__2_2_113_0
Cimasoni, David. Kac–Ward operators, Kasteleyn operators, and $s$-holomorphicity on arbitrary surface graphs. Annales de l’Institut Henri Poincaré D, Tome 2 (2015) no. 2, pp. 113-168. doi : 10.4171/aihpd/16. https://www.numdam.org/articles/10.4171/aihpd/16/

Cité par Sources :