P. Lallemand

Lattice BGK Models for Navier-Stokes Equation

We propose the lattice BGK models, as an alternative to lattice gases or the lattice Boltzmann equation, to obtain an efficient numerical scheme for the simulation of fluid dynamics. With a properly chosen equilibrium distribution, the Navier-Stokes equation is obtained from the kinetic BGK equation at the second-order of approximation. Compared to lattice gases, the present model is noise-free, has Galileian invariance and a velocity-independent pressure. It involves a relaxation parameter that influences the stability of the new scheme. Numerical simulations are shown to confirm the speed of sound and the shear viscosity.

Phase Diagrams in f.c.c. Binary Alloys: Frustration Effects

New Monte Carlo results of phase diagrams in f.c.c. binary alloys are shown. In particular, when only nearest-neighbour (nn) interactions exist, we find the triple point at a finite temperature, providing a definite answer to the long-standing controversy about its location. A new, spin-glass–like phase is found when competing next nn interactions are included.

Spin-glass transition in Heisenberg spin system with ±J random bonds

We investigate by Monte Carlo simulations the simple cubic lattice with Heisenberg spins interacting via short range ±J random bonds for different antiferromagnetic bond concentrations x. We find that for x<0.25, a transition of the para-ferromagnetic type occurs. For 0.25⪅x⩽0.5, the existence of a remanant magnetization and of a rounded peak of the specific heat together with other data support a paramagnetic-spin-glass transition at finite temperature.

Dispersion Effects in Lattice Gases with Internal and Translational Mode Coupling

We construct a 7-bit lattice-gas automaton modelling a 2D fluid with internal degrees of freedom weakly coupled to the translational degrees of freedom. The coupling is obtained by using probabilistic collision rules and produces an additional mode for density fluctuations whose effects are evidenced by the line shape of the dynamic structure factor; the spectrum of density fluctuations shows the usual normal modes together with an additional mode and a dispersion effect for the acoustic waves. Good agreement is found between these predictions and measurements performed in a direct simulation of the lattice gas dynamics.

Unusual finite size effects on critical temperature in fcc Ising antiferromagnets

A new multispin coding technique is presented for Monte Carlo simulation of antiferromagnetic Ising spin systems on an fcc lattice. The nearest‐ and next‐nearest‐neighbor interactions J1 and J2 are included. This technique allows a considerable gain in CPU time and computer memory. As a first application, we have studied samples of 4L3 spins with L up to 48. An unusual behavior of the critical temperature with increasing L is found in the case of nearest‐neighbor interaction in zero field. Finite size effects on the locations of tricrical points in the (T,J2/J1) plane are discussed.

Nature of transitions in uniformly frustrated two‐dimensional planar spin systems

We have investigated a generalized Villain’s model by varying the strength η of the negative bond. We show that there exists a critical value ηc= (1)/(3) below which the twofold degeneracy disappears; the ground state becomes ferromagnetic. A detailed numerical study shows that, for a given η>ηc, the system exhibits in general, two distinct transitions: The low temperature one corresponds to Ising‐type transition; the high temperature one corresponds to KT type. These two transitions seem to coincide in the Villain’s model (η=1). Comparison with recent related models is presented.