Related papers: Connection formulas for the lambda generalized Isi…
We study linear relations among correlation functions on a lattice obtained from integration-by-parts identities. We use the framework of twisted cocycles and determine for a scalar theory a basis of correlation functions, in which all…
This paper evaluates some generalised Euler sums involving the digamma function.
The correlation function of two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor representation are…
A method for proving the Luther-Peschel formula for the short distance asymptotics of the Ising model scaling functions is sketched.
We show a connection formula for the $q$-confluent hypergeometric functions ${}_2\varphi_1(a,b;0;q,x)$. Combining our connection formula with Zhang's connection formula for ${}_2\varphi_0(a,b;-;q,x)$, we obtain the connection formula for…
It is shown that the ratios of the quenched averaged three and four-point correlation functions of the local energy density operator to the connected ones in the random-bond Ising model approach asymptotically to some $universal$ functions.…
Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlev\'e equation as $t\to\imath\infty$ are found. These asymptotics are parameterized by monodromy data of the associated linear ODE. $$…
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
Legendre's relation for the complete elliptic integrals of the first and second kinds is generalized. The proof depends on an application of the generalized trigonometric functions and is alternative to the proof for Elliott's identity.
We review developments made since 1959 in the search for a closed form for the susceptibility of the Ising model. The expressions for the form factors in terms of the nome $q$ and the modulus $k$ are compared and contrasted. The $\lambda$…
The correlation functions of the Z-invariant Ising model are calculated explicitly using the Vertex Operators language developed by the Kyoto school.
The short distance asymptotics of the Ising Model scaling functions are computed for the scaling functions that arise as continuum limits of lattice correlations from below the critical temperature.
The functional relation of the Hurwitz zeta function is proved by using the connection problem of the confluent hypergeometric equation.
Occupation probabilities for primary-secondary-primary cell strings and correlation functions for primary sites of a decorated lattice model are expressed through the well-studied partition function and correlation functions of the Ising…
We consider spin-spin correlation functions for spins along a row, $R_n = \langle \sigma_{0,0}\sigma_{n,0}\rangle$, in the two-dimensional Ising model. We discuss a method for calculating general-$n$ expressions for coefficients in…
Continuing our work hep-th/9609135 where a explicit formula for the two-point functions of the two dimensional Z-invariant Ising model were found. I obtain here different results for the higher correlation functions and several consistency…
We introduce a class of association schemes that generalizes the Hamming scheme. We derive generating functions for their eigenvalues, and use these to obtain a version of MacWilliams theorem.
Integral formulae for the correlation functions of the XYZ model with a boundary are calculated by mapping the model to the bosonized boundary SOS model. The boundary K-matrix considered here coincides with the known general solution of the…
An explicit formula for a strong connection form in a principal extension by a coseparable coalgebra is given.