Developed after a meeting at the Santa Fe Institute on extinction modeling, this book comments critically on the various modeling approaches. In the last decade or so, scientists have started to examine a new approach to the patterns of evolution and extinction in the fossil record. This approach may be called "statistical paleontology," since it looks at large-scale patterns in the record and attempts to understand and model their average statistical features, rather than their detailed structure. Examples of the patterns these studies examine are the distribution of the sizes of mass extinction events over time, the distribution of species lifetimes, or the apparent increase in the number of species alive over the last half a billion years. In attempting to model these patterns, researchers have drawn on ideas not only from paleontology, but from evolutionary biology, ecology, physics, and applied mathematics, including fitness landscapes, competitive exclusion, interaction matrices, and self-organized criticality. A self-contained review of work in this field.

The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.

This book provides an introduction to Monte Carlo simulations in classical statistical physics aimed both at students beginning work in the field and at more experienced researchers who wish to learn more about Monte Carlo methods. The material covered includes methods for both equilibrium and out of equilibrium systems, and common algorithms like the Metropolis and heat-bath algorithms. Also discussed are more sophisticated methods such as continuous time Monte Carlo, cluster algorithms, multigrid methods, entropic sampling and simulated tempering.