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Manuscript Title: Monte Carlo optimization applied to symmetry breaking.
Authors: J.S. Kim, J.C. Toledano, P. Toledano
Program title: MCMIN
Catalogue identifier: ADHM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 109(1998)207
Programming language: Fortran, C.
Computer: SUN4m.
Operating system: UNIX, VMS.
RAM: 1500K words
Word size: 32
Keywords: Particle physics, Elementary, Computing.
Classification: 11.1.

Nature of problem:
We present a Monte Carlo optimization algorithm to search for the boundary points of the orbit space which is important in determining the symmetry breaking directions in the Higgs potential and the Landau potential. Our algorithm is robust and generally applicable. For large problems we have also developed a parallel version. We apply the method to the Landau potential of the d-wave abnormal superconductor, He-3, and a SU(5) Higgs potential.

Solution method:
THe program initially samples orbit points and computes the center of gravity of these points. It then selects the most outward points along angular rays. Then these random walkers are allowed to make random moves and the outward movement is encouraged using the rejection method. When a random walker strays into other angular ray, its position is compared with that of incumbent random walker and the one which is more outward is selected. All rays are surveyed and the procedure is repeated several times until a deviation function falls below the preset limit.

The size of the array XABIN(NB,D), where NB is the number of angular bins and D is the dimension of the representation, can be huge for a large dimensional representation. Since the program works all right with 36 <= NB <= 720, the user may reduce NB to a small number in such cases.

Running time:
The running time depends on the number of angular bins Dpts and the number of sweeps Rpts. With Dpts=360 and Rpts=10, the program takes about 10 secs in the case of He-3 on SUN4m at 100 Mhz. The timings for the parallel version is given in Table VI of the text.