Our understanding of the basic processes of crystal growth has meanwhile reached the level of maturity at least in the phenomenological concepts. This concerns for example the growth of pure crystals from a low-density nutrient phase like vapor or dilute solution with various aspects of pattern formation like spiral and layer growth, facetting and roughening, and the stability of smooth macroscopic shapes, as well as basic mechanisms of impurity incorporation in melt growth of (in this sense) simple materials like silicon or organic model substances. In parallel the experimental techniques to quantitatively ana lyze the various growth mechanisms have also reached a high level of reproducibility and precision, giving reliable tests on theoretical predictions. These basic concepts and appli cations to experiments have been recently reviewed by one of us (A. A. C. ) in "Modern Crystallography III. Crystal Growth" (Springer Series on Solid State Sciences, 1983). It has to be emphasized, however, that for practical applications we are still unable to quantitatively calculate many important parameters like kinetic coefficients from first principles. For mixed systems such as complex oxides, solutions and systems with chemi cal reactions, our degree of understanding is even lower. As a few examples for present achievements we note that experiments with vapour and molecular beam condensation of alkali halides confirmed the qualitatively predicted mechanisms of screw dislocations and two-dimensional nucleation for layer-growth.

Monte Carlo computer simulations are now a standard tool in scientific fields such as condensed-matter physics, including surface-physics and applied-physics problems (metallurgy, diffusion, and segregation, etc. ), chemical physics, including studies of solutions, chemical reactions, polymer statistics, etc., and field theory. With the increasing ability of this method to deal with quantum-mechanical problems such as quantum spin systems or many-fermion problems, it will become useful for other questions in the fields of elementary-particle and nuclear physics as well. The large number of recent publications dealing either with applications or further development of some aspects of this method is a clear indication that the scientific community has realized the power and versatility of Monte Carlo simula tions, as well as of related simulation techniques such as "molecular dynamics" and "Langevin dynamics," which are only briefly mentioned in the present book. With the increasing availability of recent very-high-speed general-purpose computers, many problems become tractable which have so far escaped satisfactory treatment due to prac tical limitations (too small systems had to be chosen, or too short averaging times had to be used). While this approach is admittedly rather expensive, two cheaper alternatives have become available, too: (i) array or vector processors specifical ly suited for wide classes of simulation purposes; (ii) special purpose processors, which are built for a more specific class of problems or, in the extreme case, for the simulation of one single model system."

Deals with the computer simulation of complex physical sys- tems encounteredin condensed-matter physics and statistical mechanics as well as in related fields such as metallurgy, polymer research,lattice gauge theory and quantummechanics.

In the seven years since this volume first appeared. there has been an enormous expansion of the range of problems to which Monte Carlo computer simulation methods have been applied. This fact has already led to the addition of a companion volume ("Applications of the Monte Carlo Method in Statistical Physics", Topics in Current Physics. Vol . 36), edited in 1984, to this book. But the field continues to develop further; rapid progress is being made with respect to the implementation of Monte Carlo algorithms, the construction of special-purpose computers dedicated to exe cute Monte Carlo programs, and new methods to analyze the "data" generated by these programs. Brief descriptions of these and other developments, together with numerous addi tional references, are included in a new chapter , "Recent Trends in Monte Carlo Simulations" , which has been written for this second edition. Typographical correc tions have been made and fuller references given where appropriate, but otherwise the layout and contents of the other chapters are left unchanged. Thus this book, together with its companion volume mentioned above, gives a fairly complete and up to-date review of the field. It is hoped that the reduced price of this paperback edition will make it accessible to a wide range of scientists and students in the fields to which it is relevant: theoretical phYSics and physical chemistry , con densed-matter physics and materials science, computational physics and applied mathematics, etc.