High-temperature expansions are derived for the specific heat and the χzz element of the susceptibility tensor for a linear chain of spins 12 with anisotropic nearest-neighbour interactions. (The coupling constants J1, J2 and J3 are chosen to be different.) Use is made of exact results of the...

We present a generalization of the direct linearization method for the Kadomtsev-Petviashvili (KP) equation and its lattice analogues such as the two-dimensional Toda equation. The generalization consists of a Riemann-Hilbert type of integral transform which relates solutions of the associated...

The exact result for the free energy per particle in systems described by a hamiltonian of the type NP(VN), where NVN denotes a set of short-range operators, is reformulated in terms of a convex-envelope construction. A comparison is given with results obtained for classical systems with...

A rigorous closed set of differential equations is derived for the correlations between x- and y-components of spins for the inhomogeneous XY-model with spin 12 in the high-temperature limit. The correlations can also be derived from a Lagrangian which describes the motion in a classical lattice...

We continue the investigation of the continuum limit properties of discrete versions of the Kadomtsev-Petviashvili (KP) equation. Using a multiple-time scale expansion, in which one of the discrete variables is replaced by an infinite number of continous variables, we can derive a hierarchy of...

Two sets of nonlinear differential equations are derived and discussed for the time-dependent correlations between x-components of spins (S = 12) in an Ising chain in the presence of a transverse magnetic field. The equations are independent of temperature which enters only through the initial...

The relations between three different symbolic descriptions of fully developed chaos in iterated one-hump maps on the interval are investigated in the case of short memory time.

The structure of the time-dependent xx-correlation functions of the one-dimensional XY-model is investigated in some detail on the basis of an extension of the thermodynamic Wick theorem. The results amount to a generalization of a rigorous result for the autocorrelation function of the...

We use the ƒ(a) (spectral dimension) formalism to give a global description of the crossover from conservative to dissipative scaling behaviour in period doubling systems. As a generic model we consider the two-dimensional Hénon map, for which the jacobian 0 ⩽ B ⩽ 1 measures the amount of...

Two types of linear inhomogeneous integral equations, which yield solutions of a broad class of nonlinear evolution equations, are investigated. One type is characterized by a two-fold integration with an arbitrary measure and contour over a complex variable k, and thier complex conjugates,...