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Manuscript Title: Efficient implementation of the Monte Carlo method for lattice gauge theory calculations on the Floating Point Systems FPS-164.
Authors: K.J.M. Moriarty, J.E. Blackshaw
Program title: LATTICE
Catalogue identifier: ACEK_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 29(1983)155
Programming language: Fortran.
Computer: DEC VAX 11/780 AND.
Operating system: DEC VAX 11/780: VMS 2.4, FPS-164 : SJE - RLE C.
RAM: 124K words
Word size: 64
Keywords: Elementary, Particle physics, Qcd, Lattice gauge theory, Yang-mills theory, Non-abelian gauge theory, Su(6) and su(6)/z6 Gauge theories, Su(n) and su(n)/zn Guage theories, Phase transitions, Statistical mechanics, Monte carlo methods.
Classification: 11.5.

Nature of problem:
The computer program calculates the average action per plaquette for SU(6)/Z6 lattice gauge theory. By considering quantum field theory on a space-time lattice, the ultraviolet divergences of the theory are regulated through the finite lattice spacing. The continuum theory results can be obtained by a renormalization group procedure. Making use of the FPS Mathematics library (MATHLIB), we are able to generate an efficient code for the Monte Carlo algorithm for lattice gauge theory calculations which compares favourably with the performance of the CDC 7600.

Solution method:
Pure SU(6)/Z6 gauge theory is simulated by Monte Carlo methods on a four dimensional space-time lattice. The system is equilibrated by the method of Metropolis et al. The FPS Mathematics Library (MATHLIB) is used to take advantage of the Floating Point Systems hardware to provide the highest speed of computation.

The only restrictions on the program are those imposed by storage limitations. The number of links in the program is given by
where D is the space-time dimensionality and ISIZE is the number of lattice sites in any direction. The SU(N) matrices are complex unitary unimodular matrices with N**2 elements. Thus, the link matrix array has dimensions
This is the largest array in the program and effectively sets the limitations on the gauge group and the size of the lattice which can be considered.