We take the occasion of this article to review 100 years of the physical and mathematical
study of the Ising model. The model, introduced by Lenz in 1920, has been at the …

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 …

Parafermionic observables and their applications to planar statistical physics models Page 1 i
i “parafermion” — 2014/1/13 — 12:09 — page 1 — #1 i i i i i i SOCIEDADE BRASILEIRA DE …

We prove universality of spin correlations in the scaling limit of the planar Ising model on
isoradial graphs with uniformly bounded angles and Z-invariant weights. Specifically, we …

We provide a simple characterization of the critical temperature for the Ising model on an
arbitrary planar doubly periodic weighted graph. More precisely, the critical inverse …

Motivated by Gutzwiller's semiclassical quantization, in which unstable periodic orbits of low-
dimensional deterministic dynamics serve as a WKB'skeleton'for chaotic quantum …

The 2d ferromagnetic Ising model was solved by Onsager on the square lattice in 1944, and
an explicit expression of the free energy density $ f $ is presently available for some other …

Isoradial embeddings of planar graphs play a crucial role in the study of several models of
statistical mechanics, such as the Ising and dimer models. Kenyon and Schlenker give a …

We show that specific exponential bivariate integrals serve as generating functions of
labeled edge-bicolored graphs. Based on this, we prove an asymptotic formula for the …

We present a new combinatorial approach to the Ising model incorporating arbitrary bond
weights on planar graphs. In contrast to existing methodologies, the exact free energy is …