Related papers: The Ising correlation $C(M,N)$ for $\nu=-k$
Using the Painlev\'{e} analysis, we investigate the integrability properties of a system of two coupled nonlinear Schr\"{o}dinger equations that describe the propagation of orthogonally polarized optical waves in an isotropic medium.…
Correlation functions in the O(n) models below the critical temperature are considered. Based on Monte Carlo (MC) data, we confirm the fact stated earlier by Engels and Vogt, that the transverse two-plane correlation function of the O(4)…
The degenerate third Painlev\'{e} equation, $u^{\prime \prime} = \frac{(u^{\prime})^{2}}{u} - \frac{u^{\prime}}{\tau} + \frac{1}{\tau}(-8 \epsilon u^{2} + 2ab) + \frac{b^{2}}{u}$, where $\epsilon,b \in \mathbb{R}$, and $a \in \mathbb{C}$,…
We show and give the linear differential operators ${\cal L}^{scal}_q$ of order q= n^2/4+n+7/8+(-1)^n/8, for the integrals $I_n(r)$ which appear in the two-point correlation scaling function of Ising model $ F_{\pm}(r)= \lim_{scaling} {\cal…
Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations in directions perpendicular and parallel to the ordering wave-vector even above the magnetic…
In this paper, we carry out in-depth research centering around the Harnack inequality for positive solutions to nonlinear heat equation on Finsler metric measure manifolds with weighted Ricci curvature ${\rm Ric}_{\infty}$ bounded below.…
The influence of finite temperatures and pairing correlations on the ground state properties of multi $\Lambda$- Ca, Sn and Pb hypernuclei is explored using finite temperature Hartree Fock Bogoliubov approach and contact pairing…
We propose a modification of the AKNS hierarchy that includes the "modified" Pohlmeyer-Lund-Regge (mPLR) equation. Similarity reductions of this hierarchy give the second, third, and fourth Painlev\'e equations. Especially, we present a new…
In this work, we establish a connection between the extended Prelle-Singer procedure with other widely used analytical methods to identify integrable systems in the case of $n^{th}$-order nonlinear ordinary differential equations (ODEs). By…
We study numerically the magnetic susceptibility of the hierarchical model with Ising spins ($\sigma =\pm 1$) above the critical temperature and for two values of the epsilon parameter. The integrations are performed exactly, using…
The thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, only the minimum of the effective potential can be…
Roy-equation analyses on lattice data of $\pi\pi$ scattering phase shifts at $m_\pi=391$MeV reveals that the lowest $f_0$ meson becomes a bound state under this condition. In addition, there is a pair of complex poles below threshold…
We rigorously derive the Ornstein-Zernike asymptotics of the pair-correlation functions for finite-range Ising ferromagnets in any dimensions and at any temperature above critical.
Recent studies have revealed much of the mathematical structure of the static correlation functions of the XXZ chain. Here we use the results of those studies in order to work out explicit examples of short-distance correlation functions in…
Noncompact SO(1,N) sigma-models are studied in terms of their large N expansion in a lattice formulation in dimensions d \geq 2. Explicit results for the spin and current two-point functions as well as for the Binder cumulant are presented…
Effective interactions that violate Newton's third law of action-reaction symmetry are common in systems where interactions are mediated by a non-equilibrium environment. Extensive Monte Carlo simulations are carried out on a…
Using non-equilibrium renormalized perturbation theory to second order in the renormalized Coulomb repulsion, we calculate the lesser $\Sigma^<$ and and greater $\Sigma^>$ self-energies of the impurity Anderson model, which describes the…
Two-point correlation functions are ubiquitous tools of modern cosmology, appearing in disparate topics ranging from cosmological inflation to late-time astrophysics. When the background spacetime is maximally symmetric, invariance…
We analyse the low temperature phase of ferromagnetic Kac-Ising models in dimensions $d\geq 2$. We show that if the range of interactions is $\g^{-1}$, then two disjoint translation invariant Gibbs states exist, if the inverse temperature…
We report the conjectures on the three-dimensional (3D) Ising model on simple orthorhombic lattices, together with the details of calculations for a putative exact solution. Two conjectures, an additional rotation in the fourth curled-up…