Nicholas Metropolis - Monte Carlo Method

Monte Carlo Method

At Los Alamos, in the 1950s, a group of researchers led by Metropolis, including John von Neumann and Stanislaw Ulam, developed the Monte Carlo method. Generally speaking, the Monte Carlo method is a statistical approach to solve deterministic many-body problems. In 1953 Metropolis co-authored the first paper on a technique that was central to the method now known as simulated annealing. This landmark paper showed the first numerical simulations of a liquid. The algorithm for generating samples from the Boltzmann distribution was later generalized by W.K. Hastings to become the Metropolis-Hastings algorithm. He is credited as part of the team that came up with the name Monte Carlo method in reference to a colleague's relative's love for the Casinos of Monte Carlo. Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. In statistical mechanics applications prior to the introduction of the Metropolis algorithm, the method consisted of generating a large number of random configurations of the system, computing the properties of interest (such as energy or density) for each configuration, and then producing a weighted average where the weight of each configuration is its Boltzmann factor, where is the energy, is the temperature, and is the Boltzmann constant. The key contribution of the Metropolis paper was the idea that

Instead of choosing configurations randomly, then weighting them with exp(−E/kT), we choose configurations with a probability exp(−E/kT) and weight them evenly.

— Metropolis et al.,