Recent monte carlo calculations of the equation of state of Lenard-Jones and hard sphere molecules

Abstract

The investigations repor ted at this sympos ium are in the process of publication elsewhere [1, 2]; since the la t te r papers are r a the r detailed, we will content ourselves here with a ra ther brief survey of the work, with only a few addit ional results. The t e rm (~ Monte Carlo ,) has come into use to designate numerical methods in which specifically stochastic elements are introduced, in contras t to the whole body of classical numerical techniques which consist of numerical evaluations of complete ly de te rminan t algebraic expressions. The par t icular Monte Carlo me thod used here was devised by METROPOHS et al. [3]; its essential fea ture is t ha t i t produces a Markov chain [4] in which the individual 5 Ia rkov s tates are points in the usual configuration space of s tat is t ical mechanics, for a sys tem of N molecules confined a t a t e m p e r a t u r e T in ~ volume Y. The t ransi t ion probabil i t ies character izing the Markov chain are de termined in such a way tha t the va lue of any funct ion of configuration state, averaged over all s tates developed in the Markov cha.in, approaches the pe t i t canonical ensemble average value of the same function. I t should be noticed t ha t the present me thod does no t consist in an evaluat ion of the configurational phase in tegral b y means of a random, selection of points in configuration space. A me thod of the l a t t e r sort, which m a y be compared with a sequence of independent throws of a die, is indeed