A quantum generalization of the Niemeijer and van Leeuwen (N-vL) renormalization group transformation is constructed which allows to study the critical properties (at Tc0) of a two-dimensional Ising system with a transverse field on a triangular lattice. Explicit calculations are performed in a...

In continuation of previous work we extend the class of two-body potentials, either repulsive or of generalized Lennard-Jones type, for which it can be proved that among all configurations of an infinite one-dimensional system of interacting particles (with fixed density in the case of repulsive...

The two-point correlation function Ĝ (q, ξ) is calculated in the critical region of momentum space q in terms of a suitable correlation lenght ξ, by means of perturbation expansion to order 1/n, for an n-vector system with long-range interactions decaying as |R/a|−(d + σ), for |R/a| å 1,...

The notion of first order phase transitions is examined for systems under external constraints. It is emphasized that only discontinuities with respect to “natural” variables (additive extensive variables and their conjugate internal forces) should be regarded as first order transitions. The...

It is shown that the coefficients of friction and diffusion of the Balescu-Lenard equation can be derived from two “generalized Rosenbluth potentials”, which reduce to the standard Rosenbluth potentials if wave effects are neglected. The potentials are evaluated explicitly in the case of...

The coefficient in the t−32 asymptotics of the time autocorrelation functions are successively determined in the framework of the non-linear Boltzmann-Enskog model. The validity of the mode-mode formula with the Enskog transport coefficients is confirmed up to first order in density.

The common statements of the Gibbs adsorption equation, and a phenomenological theory of interfaces (van der Waals, Cahn-Hilliard theory), are summarized, and then two remarks are made. The first is that only certain identifications of the local energy and entropy densities are admissible in the...

A functional integral expression of the two gate probability distribution function is obtained and the integral is performed in a “semiclassical” approximation. Based on this approximation, it is shown that the expression of the many gate probability distribution function in terms of two...

We compute exactly the transverse time-dependent spin-spin correlation functions 〈Sx1(0)SxR+1(t)〉 and 〈Sy1(0)SyR+1(t)〉 at zero temperature for the one-dimensional XY model that is defined by the hamiltonian HN = - ΣNi=1 [(1 + γ)SxiSxi+1 + (1 − γ)SyiSyi+1 + hSzi]. We then analyze...

A method of calculating the asymptotic behaviour of the higher-order correlation functions for large distances is proposed for the planar Ising model in the absence of a magnetic field. The three-point correlation functions composed of a spin operator or of energy-density operators are...