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...

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...

Explicit expressions are derived for the time correlations between x- and y-components of spin and their frequency-Fourier transforms in the one-dimensional XY-model in the high-temperature limit (β = 0). The results can be expressed as a linear combination of at most three Gaussians multiplied...

In this paper we give an exact evaluation of the free energy per particle for systems with separable many-particle interactions described by a hamiltonian of the type H = ∑kT(k) + NP (N-1 ∑k V(k)), where P is an arbitrary polynomial. In the proof use is made of a fundamental theorem due to...

The one-dimensional anisotropic XY model with alternating nearest-neighbour interactions and magnetic moments is investigated. The singularities of the susceptibility χzz in the ground state are studied in detail. In the general anisotropic case χzz can exhibit two logarithmic singularities at...

The critical behaviour of a reference system with short-range interactions under small perturbations is investigated in detail for the special case of two (relevant) thermodynamic fields h1 and h2. As reference system we choose Schofield's linear model and we consider perturbations of the type...

Explicit expressions for the time-dependent spin correlation functions are derived for the one-dimensional alternating XY-model in zero field. The ergodic properties of the wave-number dependent magnetization are discussed. It is found that the magnetization is ergodic, apart from exceptional...

Exact expressions are derived for the time-dependent correlation functions of the x and y component of the magnetization for the one-dimensional anisotropic XY-model (S=12) in zero field in the high-temperature limit. As a corollary, the correlation functions for the Ising chain in a transverse...

The treatment of a previous paper on systems with many-particle interactions is generalized to hamiltonians containing an analytic function of a number of short-range interaction operators V, which are normalized. An exact expression for the free energy per particle in the thermodynamic limit...