Within this book we have attempted to elucidate the essential features of Monte Carlo simulations and their application to problems in statistical physics. We have attempted to give the reader practical advice as well as to present theor-etically based background for the methodology of the simulations as well as the tools of analysis. New Monte Carlo methods will be devised and will be used with more powerful computers, but we believe that the advice given to the reader in Section 4.8 will remain valid.

In general terms we can expect that progress in Monte Carlo studies in the future will take place along two different routes. First, there will be a continued advancement towards ultra high resolution studies of relatively simple models in which critical temperatures and exponents, phase boundaries, etc., will be examined with increasing precision and accuracy. As a consequence, high numerical resolution as well as the physical interpretation of simulational results may well provide hints to the theorist who is interested in analytic investigation. On the other hand, we expect that there will be a tendency to increase the examination of much more complicated models which provide a better approximation to physical materials. As the general area of materials science blossoms, we anticipate that Monte Carlo methods will be used to probe the often complex behavior of real materials. This is a challenge indeed, since there are usually phenomena which are occurring at different length and time scales. As a result, it will not be surprising if multiscale methods are developed and Monte Carlo methods will be used within multiple regions of length and time scales. We encourage the reader to think of new problems which are amenable to Monte Carlo simulation but which have not yet been approached with this method.