相关论文: The critical Z-invariant Ising model via dimers: l…

The partition function of the square lattice Ising model on the rectangle with open boundary conditions in both directions is calculated exactly for arbitrary system size $L\times M$ and temperature. We start with the dimer method of…

In this paper, we use the dimer method to obtain the free energy of Ising models consisting of repeated horizontal strips of width $m$ connected by sequences of vertical strings of length $n$ mutually separated by distance $N$, with $N$…

We obtain the diagonal reflection matrices for a recently introduced family of dilute ${\rm A}_L$ lattice models in which the ${\rm A}_3$ model can be viewed as an Ising model in a magnetic field. We calculate the surface free energy from…

The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…

We study the eight-vertex model at its free-fermion point. We express a new "switching" symmetry of the model in several forms: partition functions, order-disorder variables, couplings, Kasteleyn matrices. This symmetry can be used to…

We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar or embedded on the torus. The set of positive face weights…

Fisher established an explicit correspondence between the 2-dimensional Ising model defined on a graph $G$ and the dimer model defined on a decorated version $\GD$ of this graph \cite{Fisher}. In this paper we explicitly relate the dimer…

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 temperature \beta for a graph G with coupling constants…

We present Monte Carlo simulation results for the dynamical critical exponent $z$ of the two-dimensional kinetic Ising model using a lattice of size $10^6 \times 10^6$ spins. We used Glauber as well as Metropolis dynamics. The $z$-value of…

We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and $Z(N<5)$ models. It also…

Using the formalism of differential equations, we introduce a new method to continuously deform the $s$-embeddings associated with a family of Ising models as their coupling constants vary. This provides a geometric interpretation of the…

We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic…

The free energy and local height probabilities of the dilute A models with broken $\Integer_2$ symmetry are calculated analytically using inversion and corner transfer matrix methods. These models possess four critical branches. The first…

In this essay, we briefly discuss recent developments, started a decade ago in the seminal work of Smirnov and continued by a number of authors, centered around the conformal invariance of the critical planar Ising model on $\mathbb{Z}^2$…

Motivated by recent numerical findings [M. Henkel, T. Enss, and M. Pleimling, J. Phys. A: Math. Gen. 39 (2006) L589] we re-examine via Monte Carlo simulations the linear response function of the two-dimensional Ising model with Glauber…

A class of generalized Ising models is examined with a view to extracting a low energy sector comprising Dirac fermions coupled to Yang-Mills vectors. The main feature of this approach is a set of gap equations, covariant with respect to…

We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings,…

The Ising model, in presence of an external magnetic field, is isomorphic to a model of localized interacting particles satisfying the Fermi statistics. By using this isomorphism, we construct a general solution of the Ising model which…

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 expressed as the determinant of a set of ordered and…

We show that the one dimensional, critical transverse field Ising model is Yang-Baxter integrable. This is done by constructing commuting transfer matrices built out of a $R$-matrix satisfying the Yang-Baxter equation with additive spectral…