For a one-dimensional system of classical spins with nearest neighbour Heisenberg interaction we derive the equation of motion for each three-dimensional spin vector. In the continuum limit where the spins lie dense on a line this set of equations reduces to a nonlinear partial differential...

A systematic approximation scheme is proposed for the evaluation of the determinant of an infinite-dimensional matrix which is encountered with, for example, in the theoretical study of Fermion aggregate. This scheme is compatible with the cluster variation method for Ising problems since the...

The behavior of a Knudsen gas between two plates at unequal temperatures is discussed. A general formulation is given for the case of small temperature difference. The use of perturbation theory is then demonstrated and applied to the case of a nonspherical interaction of a polyatomic gas with...

An approximate value for the ground-state energy of an antiferromagnetic lattice of spins one-half is determined by means of a repeated renormalization procedure in which the lattice is divided into cells with an effective interaction. This effective interaction is determined on the basis of the...

Generalized Clausius-Clapeyron relations are derived for discontinuous orientational phase transitions in the quantum-mechanical regime. Some qualitative features of the isotope effect on the transition temperature are explained. The quantum correction to the density dependence of the...

Based on the Klimontovich method of construction of a relativistic statistical mechanics the binary correlation function of a relativistic plasma is considered. Up to the order e4 for spatially homogeneous systems the relativistic binary correlation function can be expressed by the relativistic...

In generalizing a continuum approximation suggested by Ferrell for a spatially homogeneous Ising model, some results of earlier, exact calculations concerning the critical thermodynamics of certain spatially non-homogeneous 2d Ising systems are reproduced in a more transparent way, and the...

Series expansions are derived for the free energy and the fluctuations of a generalized hamiltonian. These series are analysed in the special case of the XY hamiltonian on an f.c.c. lattice in an external parallel magnetic field. The critical indices seem to be independent of the field.

A plasma and a neutral fluid behave in very different ways in the so-called hydrodynamical limit, when submitted to a long-wavelength disturbance. Both cases can be treated however in the same way if the plasma-dynamical equations are properly regularized. The frequencies and damping rates of...

We explore the consequences of the existence of a group of linear symmetry transformations for the sixteen-vertex model. An arbitrary sixteen-vertex model is shown tobe equivalent to a standard model, described in terms of ten parameters having an invariant significance. The general eight-vertex...