相关论文: Square lattice Ising model susceptibility: connect…
We present a simple, but efficient, way to calculate connection matrices between sets of independent local solutions, defined at two neighboring singular points, of Fuchsian differential equations of quite large orders, such as those found…
We first study the properties of the Fuchsian ordinary differential equations for the three and four-particle contributions $ \chi^{(3)}$ and $ \chi^{(4)}$ of the square lattice Ising model susceptibility. An analysis of some mathematical…
Using an expansion method in the variables $ x_i$ that appear in the $(n-1)$-dimensional integrals representing the $n$-particle contribution to the Ising square lattice model susceptibility $\chi$, we generate a long series of coefficients…
We give the Fuchsian linear differential equation satisfied by $\chi^{(4)}$, the ``four-particle'' contribution to the susceptibility of the isotropic square lattice Ising model. This Fuchsian differential equation is deduced from a series…
In a previous paper (J. Phys. A {\bf 37} (2004) 9651-9668) we have given the Fuchsian linear differential equation satisfied by $\chi^{(3)}$, the ``three-particle'' contribution to the susceptibility of the isotropic square lattice Ising…
We calculate very long low- and high-temperature series for the susceptibility $\chi$ of the square lattice Ising model as well as very long series for the five-particle contribution $\chi^{(5)}$ and six-particle contribution $\chi^{(6)}$.…
We consider the Fuchsian linear differential equation obtained (modulo a prime) for $\tilde{\chi}^{(5)}$, the five-particle contribution to the susceptibility of the square lattice Ising model. We show that one can understand the…
We use the recently derived form factor expansions of the diagonal two-point correlation function of the square Ising model to study the susceptibility for a magnetic field applied only to one diagonal of the lattice, for the isotropic…
This paper deals with $\tilde{\chi}^{(6)}$, the six-particle contribution to the magnetic susceptibility of the square lattice Ising model. We have generated, modulo a prime, series coefficients for $\tilde{\chi}^{(6)}$. The length of the…
We introduce some multiple integrals that are expected to have the same singularities as the singularities of the $ n$-particle contributions $\chi^{(n)}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear…
We investigate the complex-temperature singularities of the susceptibility of the 2D Ising model on a square lattice. From an analysis of low-temperature series expansions, we find evidence that as one approaches the point $u=u_s=-1$ (where…
We derive low-temperature series (in the variable $u = \exp[-\beta J/S^2]$) for the spontaneous magnetisation, susceptibility and specific heat of the spin-$S$ Ising model on the square lattice for $S=\frac32$, 2, $\frac52$, and 3. We…
We recall the form factors $ f^{(j)}_{N,N}$ corresponding to the $\lambda$-extension $C(N,N; \lambda)$ of the two-point diagonal correlation function of the Ising model on the square lattice and their associated linear differential…
We give the exact expressions of the partial susceptibilities $\chi^{(3)}_d$ and $\chi^{(4)}_d$ for the diagonal susceptibility of the Ising model in terms of modular forms and Calabi-Yau ODEs, and more specifically, $_3F_2([1/3,2/3,3/2],\,…
We consider deformations of $2\times2$ and $3\times3$ matrix linear ODEs with rational coefficients with respect to singular points of Fuchsian type which don't satisfy the well-known system of Schlesinger equations (or its natural…
We use an m-vicinity method to examine Ising models on hypercube lattices of high dimensions d>=3. This method is applicable for both short-range and long-range interactions. We introduce a small parameter, which determines whether the…
The critical behavior of the 1/5-depleted square-lattice Ising model with nearest neighbor ferromagnetic interaction has been investigated by means of both an exact solution and a high-temperature series expansion study of the zero-field…
We study complex-temperature properties of the uniform and staggered susceptibilities $\chi$ and $\chi^{(a)}$ of the Ising model on the honeycomb lattice. From an analysis of low-temperature series expansions, we find evidence that $\chi$…
We have made substantial advances in elucidating the properties of the susceptibility of the square lattice Ising model. We discuss its analyticity properties, certain closed form expressions for subsets of the coefficients, and give an…
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…