Revisiting the combinatorics of the 2D Ising model
Annales de l’Institut Henri Poincaré D, Tome 4 (2017) no. 3, pp. 309-385.

We provide a concise exposition with original proofs of combinatorial formulas for the 2D Ising model partition function, multi-point fermionic observables, spin and energy density correlations, for general graphs and interaction constants, using the language of Kac–Ward matrices. We also give a brief account of the relations between various alternative formalisms which have been used in the combinatorial study of the planar Ising model: dimers and Grassmann variables, spin and disorder operators, and, more recently, s-holomorphic observables. In addition, we point out that these formulas can be extended to the double-Ising model, de�fined as a pointwise product of two Ising spin con�gurations on the same discrete domain, coupled along the boundary.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/42
Classification : 82-XX
Mots-clés : Ising model, Kac–Ward matrix, spin correlations, fermionic observables, discrete holomorphic functions, spin structures, double-Ising model 
@article{AIHPD_2017__4_3_309_0,
     author = {Chelkak, Dmitry and Cimasoni, David and Kassel, Adrien},
     title = {Revisiting the combinatorics of the {2D} {Ising} model},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {309--385},
     volume = {4},
     number = {3},
     year = {2017},
     doi = {10.4171/aihpd/42},
     mrnumber = {3713019},
     zbl = {1380.82017},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/42/}
}
TY  - JOUR
AU  - Chelkak, Dmitry
AU  - Cimasoni, David
AU  - Kassel, Adrien
TI  - Revisiting the combinatorics of the 2D Ising model
JO  - Annales de l’Institut Henri Poincaré D
PY  - 2017
SP  - 309
EP  - 385
VL  - 4
IS  - 3
UR  - http://archive.numdam.org/articles/10.4171/aihpd/42/
DO  - 10.4171/aihpd/42
LA  - en
ID  - AIHPD_2017__4_3_309_0
ER  - 
%0 Journal Article
%A Chelkak, Dmitry
%A Cimasoni, David
%A Kassel, Adrien
%T Revisiting the combinatorics of the 2D Ising model
%J Annales de l’Institut Henri Poincaré D
%D 2017
%P 309-385
%V 4
%N 3
%U http://archive.numdam.org/articles/10.4171/aihpd/42/
%R 10.4171/aihpd/42
%G en
%F AIHPD_2017__4_3_309_0
Chelkak, Dmitry; Cimasoni, David; Kassel, Adrien. Revisiting the combinatorics of the 2D Ising model. Annales de l’Institut Henri Poincaré D, Tome 4 (2017) no. 3, pp. 309-385. doi : 10.4171/aihpd/42. http://archive.numdam.org/articles/10.4171/aihpd/42/

Cité par Sources :