A new approach to Monte Carlo simulations is presented, giving a highly efficient method of simulation for large systems near criticality. The algorithm violates dynamic universality at second-order phase transitions, producing unusually small values of the dynamical critical exponent.

We present a new method for using the data from Monte Carlo simulations that can increase the efficiency by 2 or more orders of magnitude. A single Monte Carlo simulation is sufficient to obtain complete thermodynamic information over the entire scaling region near a phase transition. The accuracy of the method is demonstrated by comparison with exact results for the d=2 Ising model. New results for d=2 eight-state Potts model are also presented. The method is generally applicable to statistical models and lattice-gauge theories.

We present a new method for optimizing the analysis of data from multiple Monte Carlo computer simulations over wide ranges of parameter values. Explicit error estimates allow objective planning of the lengths of runs and the parameter values to be simulated. The method is applicable to simulations in lattice gauge theories, chemistry, and biology, as well as statistical mechanics.

A new Monte Carlo method is presented for simulations of systems with quenched random interactions. The approach greatly reduces the long correlation times characteristic of standard methods, allowing the investigation of lower temperatures with less computer time than previously necessary.

When a can containing one large ball and a number of smaller ones is shaken, the large ball rises to the top, even when the larger ball is more dense than the others. Similarly, a mixture of different sized particles will segregate by size when shaken. An adaptation of the Monte Carlo method is used to study this size segregation. The results show the local, geometric mechanism by which the segregation is produced. Segregation by size is to be distinguished from the more obvious sifting process which occurs when tiny grains filter down through the interstices between large particles.