The impact of large-scale computing on lattice statistics

Abstract

The use of computers in theoretical physics has grown dramatically over the years; this is as true in lattice statistical mechanics as anywhere. This paper is concerned with one such aspect with which the name of C. Domb has been closely associated: the enumeration of embeddings of connected structures in an unlimited crystal lattice. An informal account is given of a recent computer project originating in the combinatorial “shadow” method developed by M. F. Sykes: the determination of the numbers and the properties ofcluster embeddings in crystal lattices. Sykes' approach has opened a way to information which was earlier considered to be forever beyond reach. The principles are given and the algorithms sketched; the detailed FORTRAN programming is not given. The methods used have had to be specially developed, but some have a wider application for computer algebra when the computational task is massive. Provided the computer is large enough and fast enough, impressive results may be obtained in return for a reasonable effort. In practice, this implies that the computer may have to be one of the largest and fastest, or else that it is dedicated to the task.