Dimer models and the Ising model

This is an incomplete collection of references on dimer models and the Ising model. Some references are with commentaries. If you will see some serious omission, please let me know. I know the list is incomplete.

Interfacial tension for the Ising model and related questions:

D.B. Abraham, A. Martin-Loef, The transfer matrix for a pure phase in the two-dimensional Ising model, CMP, v. 32, 245-268, (1973) (Ising model with all boundary spins + is solved using the transfer matrix)
D.B. Abraham, G. Galovotti, A. Martin-Loef, Surface tension in the two-dimensional Ising model, Physica v. 65 (1973), 73-88. (several definitions of the surface tension between oppositely magnetized phases in 2D Ising model are examined. It is proven that all of them agree with the one given by Onsager at low temperature)
D.B. Abraham, Interface profile of the Ising ferromagnet in two dimensions, CMP, v. 49, 35-46 (1976) (the interface profile is obtained for the vertical interface).
D. Abraham, P. Reed, Diagonal interface in the two-dimensional Ising ferromagnet, J. Phys. A, v. 10, n. 6, L121-L123 (1977) (this is where the interface tension was computed for any angle, but no details are given).
D. Abraham, Structure, phase transition and dynamics of interfaces and surfaces, J. Phys. A, v. 21, 1741-1751 (1988) (the structure of fluctuations near the interface is obtained for the horizontal interface, there is a remark how to generalize this to any angle).
D.B. Abraham, P.J. Upton, Interface at general orientation in a two-dimensional Ising model, Phys. Rev. B, v. 37, n. 7, 3835-3837 (1988) (Scaling of fluctuations of the magnetization is obtained near the interface positioned at any angle. Transfer matrix method is used.)
D. Abraham, C. Newman, S. Shlosman, A continuum of pure states in the Ising model on a halfplane, J. Sat, Phys, v. 172, 611-626 (2018). (a Gibbs state exists for each interface angle)

Some pioneering papers on Dimer models:

P. W. Kasteleyn, The statistics of dimers on a lattice. Physica 27 (1961), Page 1209–1225.
P. W. Kasteleyn, Dimer statistics and phase transitions, J. Mathematical Phys. 4 (1963) 287– 293.
P. W. Kasteleyn, Graph theory and crystal physics. 1967 Graph Theory and Theoretical Physics pp. 43–110 Academic Press, London.
H. N. V. Temperley and M. E. Fisher. Dimer problem in statistical mechanics – an exact result. Philos. Mag. 6 (1961), Pages 1061–1063.
Nienhuis, B.; Hilhorst, H. J.; Bl ̈ote, H. W. J. Triangular SOS models and cubic-crystal shapes. J. Phys. A 17 (1984), no. 18, 3559–3581. (the dimer model on a hexagonal lattice as a tiling model and a hight function)

Books and surveys

R. Kenyon, An introduction to the dimer model,

D. Cimasoni, The geometry of dimer models

The Kasteleyn solution, Pfaffians and spin structures

G. Kuperberg, An exploration of the permanent-determinant method, Electron. J. Combin. 5 (1998), Research Paper 46, 34 pp. (electronic).
A. Galluccio and M. Loebl, On the theory of Pfaffian orientations. I. Perfect matchings and permanents. Electron. J. Combin. 6 (1999), Research Paper 6, 18 pp. (electronic).
G. Tesler, Matchings in graphs on non-orientable surfaces, J. Combin. Theory Ser. B 78 (2000), no. 2, 198–231.
D. Cimasoni and N. Reshetikhin, Dimers on surface graphs and spin structures.
D. Cimasoni and N. Reshetikhin, Dimers on surface graphs and spin structures.
D. Cimasoni, Dimers on graphs in non-orientable surfaces
D. Cimasoni, Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices
D.Cimasoni, Anh Minh Pham, Identities between dimer partition functions on different surfaces, J. Stat. Mech. Theory Exp. (2016), 103101.

The relation between Ising models and dimer models:

See the corresponding chapter of the book by McCoy and Wu.
D. Chelkak, D. Cimasoni, A. Kassel, Revisiting the combinatorics of the 2D Ising model.Ann. Inst. Henri Poincaré (D) Comb. Phys. Interact. (2017), 4 (3), pp. 309–385

The limit shape phenomenon:

H. Cohn and M. Larsen and J. Propp, The shape of a typical boxed plane partition. New York J. Math. 4 (1998), Page 137–165.
H. Cohn, R. Kenyon and J. Propp, A variational principle for domino tilings, J. Amer. Math. Soc. 14 (2001), no. 2, 297–346.
Kenyon, Richard; Okounkov, Andrei; Sheffield, Scott, Dimers and amoebae. Ann. of Math. (2) 163 (2006), no. 3, 1019–1056.
Kenyon, Richard and Okounkov Andrei, Limit shapes and the complex Burgers equation, Acta Math. 199 (2007), Number 2, Page 263–302.

Fluctuations near the limit shape:

K. Johansson, Non-intersecting paths, random tilings and random matrices. Probab. Theory and Related Fields 123 (2002), Number 2, Page 225–280.
R. Kenyon, The Laplacian and Dirac operators on critical planar graphs, Invent. Math. 150 (2002), no. 2, 409–439.
Okounkov, Andrei and Reshetikhin, Nikolai. Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram. J. Amer. Math. Soc. 16 (2003), 581– 603 (electronic).
Okounkov, Andrei and Reshetikhin, Nikolai. The birth of a random matrix. Moscow Mathematical Journal 6, Number 3. July-September 2006, Pages 553–566.
Okounkov, Andrei and Reshetikhin, Nikolai. Random skew plane partitions and the Pearcey process. Commun. Math. Phys., 269, (2007), 571609.
Kenyon, Richard. Height fluctuations in the honeycomb dimer model. Comm. Math. Phys. (2008).

Universality of fluctuations in the dimer model:

Nathaniel Berestycki, Benoit Laslier, Gourab Ray arXiv:1610.08021

Exact solution of the classical dimer model on a triangular lattice:

Estelle Basor, Pavel Bleher, Monomer-monomer correlations, (math-ph) arXiv:1608.03151
Arvind Ayyer, Squareness for the Monopole-Dimer model,
arXiv:1507.04193
Alexi Morin-Duchesne, Jorgen Rasmussen, Philippe Ruelle, Integrability and conformal data of the dimer model, arXiv:1105.4158
Richard Kenyon, Conformal invariance of loops in the double-dimer model arXiv:0803.2652
Boundary monomers in the dimer model Vyatcheslav B. Priezzhev, Philippe Ruelle arXiv:cond-mat/0701075
Non-Local Finite-Size Effects in the Dimer Model Nickolay Sh. Izmailian, Vyatcheslav B. Priezzhev, Philippe Ruelle, arXiv:math/0608600
Conformal invariance of isoradial dimer models & the case of triangular quadri-tilings, B. de TiliÃ¨re, arXiv:math-ph/0405052
Height fluctuations in the honeycomb dimer model Richard Kenyon (math-ph), (math.PR) arXiv:math/0310326

Resonant phenomena:

R. Kenyon, D. Wilson, Critical resonance in the non-intersecting latice path model, arXiv: math/0111199.

Some recent papers on dimer models and discrete geometry:

D. Chelkak, S. Ramassamy, Fluctuations in the Aztec diamonds via a Lorenz-Minimal surface, ArXiv: 2002.07540.
R. Kenyon, W.Y. Lam, S. Ramassamy, M. Russkikh, Dimers and circle patterns, arXiv: 1810.05616.
D. Chelkak, B. Laslier, M. Russkikh, Dimer model and holomorphic functions on T-embeddings of planar graphs.