Monte Carlo Simulations and Application to Manganite Models

Abstract

Partition functions and functional integrals (path integrals) reduce many-body problems to complicated multidimensional integrals or sums. Monte Carlo simulations are tools to evaluate in an approximate way these integrals/sums, allowing for fairly precise calculation of observables. The results are exact within statistic and controlled systematic errors. This is a powerful procedure that supplements analytical calculations. A large variety of physical properties can be studied in a wide range of parameters with relatively small effort, allowing the investigation of low, intermediate, and large coupling regimes, where analytical techniques cannot be controlled. The simulations give results that can often be directly compared with experiments, offering a method to determine if a given model contains the essential physics of a system. This allows for a systematic exploration of the relationship between microscopical models and experimental observations, varying the parameters of a model.