History of Monte Carlo Method

Fuad Said Faiz Nammas

It could be argued that current physics research could be divided into three areas - theoretical, experimental and computational. Numerical approach, in which systems are mimicked as accurately as possible using a computer or in which computer models are set up to provide well - behaved experimental systems are increasingly providing a bridge between theory and experiment, for instance; the Monte Carlo method (MC) and the molecular-dynamics method (MD). In Monte Carlo method the exact dynamical behavior of a system is replaced by a stochastic process, whereas the MD methods are based on a simpler principle and consists of solving a system of Newton's equations for an N-body system. Stochastic simulation is some times called MC simulation (simulation is a numerical technique for conducting experiment on a digital computer, which involves certain types of mathematical and logical models that describe the behavior of the system over extended period of real time). The generally accepted birth date of the MC method is 1949, when an article entitled "The Monte Carlo Method" appeared, the American mathematicians J.Neyman and S.Ulam are considered to be its originator. The first successful application of this method to a problem of statistical thermodynamics dates back only to 1953, when Metropolis and co-workers studied "fluid" consisting of hard disks. In the nineteenth and early twentieth centuries, statistical problems were sometimes solved with the help of random selections, that is, in fact, by the MC method. Prior to the appearance of electronic computers, this method was not widely applicable since the simulation of random quantities by hand is a very laborious process. Thus, the beginning of the MC method as a highly universal numerical technique became possible only with the appearance of computers.

Historically, the MC method was considered to be a technique, using random numbers, to find a solution of a model under study. Actually, what are available at computer centers are arithmetic codes for generating sequences of pseudo random digits, where each digit (0 through 9) occurs with approximately equal probability. Consequently, the sequences can model successive flips of a fair ten-side die. Such codes are called random number generators. Grouped together, these generated digits yield random numbers with any required number of digits.