Historically physics was first known as ‘natural philosophy’ and research was
carried out by purely theoretical (or philosophical) investigation. True progress
was obviously limited by the lack of real knowledge of whether or not a
given theory really applied to nature. Eventually experimental investigation
became an accepted form of research although it was always limited by the
physicist’s ability to prepare a sample for study or to devise techniques to
probe for the desired properties. With the advent of computers it became
possible to carry out simulations of models which were intractable using
‘classical’ theoretical techniques. In many cases computers have, for the
first time in history, enabled physicists not only to invent new models for
various aspects of nature but also to solve those same models without substantial
simplification. In recent years computer power has increased quite
dramatically, with access to computers becoming both easier and more common
(e.g. with personal computers and workstations), and computer simulation
methods have also been steadily refined. As a result computer
simulations have become another way of doing physics research. They provide
another perspective; in some cases simulations provide a theoretical basis
for understanding experimental results, and in other instances simulations
provide ‘experimental’ data with which theory may be compared. There are
numerous situations in which direct comparison between analytical theory
and experiment is inconclusive. For example, the theory of phase transitions
in condensed matter must begin with the choice of a Hamiltonian, and it is
seldom clear to what extent a particular model actually represents a real
material on which experiments are done. Since analytical treatments also
usually require mathematical approximations whose accuracy is difficult to
assess or control, one does not know whether discrepancies between theory
and experiment should be attributed to shortcomings of the model, the
approximations, or both. The goal of this text is to provide a basic understanding
of the methods and philosophy of computer simulations research
with an emphasis on problems in statistical thermodynamics as applied to
condensed matter physics or materials science. There exist many other simulational
problems in physics (e.g. simulating the spectral intensity reaching a
detector in a scattering experiment) which are more straightforward and
which will only occasionally be mentioned. We shall use many specific examples
and, in some cases, give explicit computer programs, but we wish to
emphasize that these methods are applicable to a wide variety of systems
including those which are not treated here at all. As computer architecture
changes the methods presented here will in some cases require relatively
minor reprogramming and in other instances will require new algorithm
development in order to be truly efficient. We hope that this material will
prepare the reader for studying new and different problems using both
existing as well as new computers.