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.
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C. Domb and M. S. Green, eds.,Phase Transitions and Critical Phenomena, Vol. 3 (Academic Press, 1974).
J. L. Martin,Proc. Camb. Philos. Soc. 58:92–101 (1962).
S. Rushbrooke and J. Eve,J. Chem. Phys. 31:1333 (1959).
M. F. Sykes,J. Phys. A 19:1007–1025, 1027–1032, 2425–2429, 2431–2437 (1986).
J. L. Martin, inPhase Transitions and Critical Phenomena, Vol. 3, C. Domb and M. S. Green, eds., (Academic Press, 1974), pp. 97–112.
W. F. Lunnon, inComputers in Number Theory, A. O. L. Atkin and B. J. Birch, eds. (Academic Press, 1971); D. H. Redelmeier,Discrete Math. 36:191–203 (1981).
D. E. Knuth,The Art of Computer Programming, Vol. 3 (Addison-Wesley, 1973), pp. 506–542.
D. F. Styer, M. D. Edwards, and E. A. Andrews,J. Phys. A 21:L1153–1156 (1988).
M. F. Sykes,J. Phys. A 19:2425–2429 (1986); Eqs. (3.2)–(3.5).
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Martin, J.L. The impact of large-scale computing on lattice statistics. J Stat Phys 58, 749–774 (1990). https://doi.org/10.1007/BF01112773
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DOI: https://doi.org/10.1007/BF01112773