Related papers: Lace expansion for the Ising model
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor…
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\lambda$, in a scaling…
Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. This amounts to a generalization from 2-point to point-link-point interactions. An associated graph theory with…
The critical dynamics of Ising spin glasses with Bimodal, Gaussian, and Laplacian interaction distributions are studied numerically in dimensions 3 and 4. The data demonstrate that in both dimensions the critical dynamic exponent $z_{\rm…
The bivariate high-temperature expansion of the spin-spin correlation-function of the three-dimensional classical XY (planar rotator) model, with spatially-anisotropic nearest-neighbor couplings, is extended from the 10th through the 21st…
In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact…
Critical phenomena in the two-dimensional Ising model with a defect line are studied using boundary conformal field theory on the $c=1$ orbifold. Novel features of the boundary states arising from the orbifold structure, including…
We apply an improved Taylor expansion method, which is a variational scheme to the Ising model in two dimensions. This method enables us to evaluate the free energy and magnetization in strong coupling regions from the weak coupling…
Extensive simulations are made of link and spin overlaps in four and five dimensional Ising Spin Glasses (ISGs). Moments and moment ratios of the mean link overlap distributions (the variance, the kurtosis and the skewness) show clear…
The fractal dimensions and the percolation exponents of the geometrical spin clusters of like sign at criticality, are obtained numerically for an Ising model with temperature-dependent annealed bond dilution, also known as the thermalized…
Extensive simulations are made of the spin glass susceptibility and correlation length in five dimension Ising Spin Glasses (ISGs) with Gaussian and bimodal interaction distributions. Once the transition temperature is accurately…
We study the critical behavior of a general class of cubic-symmetric spin systems in which disorder preserves the reflection symmetry $s_a\to -s_a$, $s_b\to s_b$ for $b\not= a$. This includes spin models in the presence of random…
The signed loop method is a beautiful way to rigorously study the two-dimensional Ising model with no external field. In this paper, we explore the foundations of the method, including details that have so far been neglected or overlooked…
The 3D Ising model and the generalized free scalar of dimension at least 0.75 belong to a continuous line of nonlocal fixed points, each referred to as a long-range Ising model. They can be distinguished by the dimension of the lightest…
We prove convergence results for variants of Smirnov's fermionic observable in the critical Ising model in presence of free boundary conditions. One application of our analysis is a simple proof of a theorem by Hongler and Kyt\"ol\"a on…
We prove a scaling limit theorem for the simple random walk on critical lattice trees in $\mathbb{Z}^d$, for $d\geq 8$. The scaling limit is the Brownian motion on the Integrated Super-Brownian Excursion (BISE) which is the same one that we…
We investigate a class of two-dimensional two-band microscopic models in which the inter-band repulsive interactions play the dominant role. We first demonstrate three different schemes of constraining the ratios between the three types of…
In this note we overview recent convergence results for correlations in the critical planar nearest-neighbor Ising model. We start with a short discussion of the combinatorics of the model and a definition of fermionic and spinor…
We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random…
We study the time evolution of the two-dimensional kinetic Ising model in finite systems with a non-conserved order parameter, considering nearest-neighbour interactions on the square lattice with periodic and open boundary conditions.…