Related papers: Correct bounds on the Ising lace-expansion coeffic…
We prove that the Fourier transform of the properly-scaled normalized two-point function for sufficiently spread-out long-range oriented percolation with index \alpha>0 converges to e^{-C|k|^{\alpha\wedge2}} for some C\in(0,\infty) above…
We derive and prove exponential and form factor expansions of the row correlation function and the diagonal correlation function of the two dimensional Ising model.
The high-temperature expansion coefficients of the ordinary and the higher susceptibilities of the spin-1/2 nearest-neighbor Ising model are calculated exactly up to the 20th order for a general d-dimensional (hyper)-simple-cubical lattice.…
We study the nearest-neighbour Ising and $\varphi^4$ models on $\mathbb Z^d$ with $d\geq 3$ and obtain new lower bounds on their two-point functions at (and near) criticality. Together with the classical infrared bound, these bounds turn…
We study connection probabilities between vertices of the square lattice for the critical random-cluster (FK) model with cluster weight 2, which is related to the critical Ising model. We consider the model on the plane and on domains…
It is shown that the partition function of the 2d Ising model on the dual finite lattice with periodical boundary conditions is expressed through some specific combination of the partition functions of the model on the torus with…
In this paper, we prove an extension theorem for spheres of square radii in $\mathbb{F}_q^d$, which improves a result obtained by Iosevich and Koh (2010). Our main tool is a new point-hyperplane incidence bound which will be derived via a…
We prove that the growth constants for nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice Zd are asymptotic to 2de as the dimension goes to infinity, and that their critical one-point functions converge to e.…
We study the analytic properties of the scaling function associated with the 2D Ising model free energy in the critical domain $T \to T_c$, $H \to 0$. The analysis is based on numerical data obtained through the Truncated Free Fermion Space…
We prove extension of a di-bar-closed, smooth, form from the intersection of a pseudoconvex domain with a complex hyperplane to the whole domain. The extension form is di-bar-closed, has harmonic coefficients and its L^2-norm is estimated…
We present a differential formulation of the recursion formula of the hierarchical model which provides a recursive method of calculation for the high-temperature expansion. We calculate the first 30 coefficients of the high temperature…
We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous…
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…
A linear growth-diffusion equation is studied in a time-dependent interval whose location and length both vary. We prove conditions on the boundary motion for which the solution can be found in exact form, and derive the explicit expression…
Using a renormalized linked-cluster-expansion method, we have extended to order $\beta^{23}$ the high-temperature series for the susceptibility $\chi$ and the second-moment correlation length $\xi$ of the spin-1/2 Ising models on the sc and…
In three dimensions, or more generally, below the upper critical dimension, scaling laws for critical phenomena seem well understood, for both infinite and for finite systems. Above the upper critical dimension of four, finite-size scaling…
A generalization of the compressible Ising model in which spins are hosted on an elastic $D$-dimensional lattice embedded in $d>D$ dimensions is studied. Two critical systems interact when temperature is tuned to the Ising transition point,…
We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size L as L^{5/4}, rather than proportional to L as in standard finite size scaling (FSS) theory. Our results confirm a…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
The two-dimensional Ising model is studied at the boundary of a half-infinite cylinder. The three regular lattices (square, triangular and hexagonal) and the three regimes (sub-, super- and critical) are discussed. The probability of having…