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We study by computer simulation the behavior at low energy of two-dimensional Lennard-Jones systems, with square or triangular cells and a number of degrees of freedom N up to 128. These systems exhibit a transition from ordered to stochastic motions, passing through a region of intermediate behavior. We thus find two stochasticity borders, which separate in the phase space the ordered, intermediate, and stochastic regions. The corresponding energy thresholds have been determined as functions of the frequency ω of the initially excited normal modes; they generally increase with ω and appear to be independent of N. Their values agree with those found by other authors for one-dimensional LJ systems. We computed also the maximal Lyapunov characteristic exponent χ* of our systems, which is a typical measure of stochasticity; this analysis shows that even in the ordered region certain stochastic features may persist. At higher energies, χ* increases linearly with the energy per degree of freedom e. The law χ*(e) has been determined in the thermodynamic limit by extrapolation. The values found for the stochasticity thresholds fall in a physically significant energy range. The behavior of the thresholds as a function of ω and N is compatible with the hypothesis on the existence of a classical zero-point energy, advanced by Cercignani, Galgani, and Scotti. © 1980 The American Physical Society

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The internal consistency of the procedure described by Rull [Phys. Rev. A 26, 2993 (1982}]to determine the thermodynamical properties of the Lennard-Jones classical fluid in the critical region on the basis of the Percus-Yevick {PY) equation is discussed and found inadequate. New results for the solution of this equation near the critical point for a much larger range in r space are presented. We consider the sum of two Yukawa potentials as the pair interaction. Our results are in complete agreement with the critical behavior found with models exactly soluble (adhesive hard spheres and lattice gas) in the PY approximation: classical critical exponents but a nonclassical scaling function that leads to an asymmetry between liquid and vapor with a true spinode present only for p & p, . %e still do not have a fully microscopic theory of the critical point of the liquid-vapor phase transition. This explains the effort that in recent years has been devoted to clarify the critical behavior given by theories developed for classical fluids the perturbative approach and the method of integral equations for the radial distribution function (RDF) g(r).The purpose of this Comment is to shed additional light on the critical behavior given by the Percus-Yevick (PY) equation starting from a reanalysis of the recent numerical solution obtained by Brey, Santos, and Rull2 for the Lennard-Jones interaction. That computation gave a completely classical critical behavior, i.e. , not only the critical exponents have classical (or mean-field) values but also the equation of state has a van der Waals form. As discussed in great detail by Fishman and Fisher, the PY equation for the adhesive hard-sphere (AHS) system, an equation that has been solved exactly by Baxter, 4 also leads to classical critical exponents, but the scaling function for the equation of state is nonclassical. In particular, it leads to a strong asymmetry between liquid and vapor even asymptotically close to the critical point and to the presence of a spinodal line only on the liquid side of the critical point. Support for the view that these nonclassical features should be generally valid for the PY equation and not due to the singular nature of the AHS interaction comes from recent analysis' of the PY equation for the lattice gas. Also in this case the equation is exactly soluble and the critical behavior has the same nonclassical features of the AHS system. Indeed, the analysis that we present here of our numerical solution of the PY equation for a fluid with an interaction of finite range gives a critical behavior similar to that found analytically for the AHS and for the lattice-gas model treated in the PY approximation. Thus only the computation of Brey et 01. 2 for the Lennard-Jones interaction gives a completely classical critical behavior. In this Comment we discuss why the approximation used by Brey et al. leads necessarily to such a critical behavior. The thermodynamical properties of a classical fluid are evaluated in terms of correlation functions via the...

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