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Manuscript Title: Measuring the string tension in random surface models with extrinsic curvature.
Authors: A. Irback, J. Jurkiewicz, S. Varsted
Program title: STRTEN
Catalogue identifier: ACGZ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 70(1992)59
Programming language: Fortran.
Computer: CRAY Y-MP.
Operating system: UNICOS.
RAM: 2600K words
Word size: 64
Peripherals: disc.
Keywords: Particle physics, Elementary, Qcd, Random surfaces, Dynamical triangulation, Extrinsic curvature, Monte carlo, Strings, String tension, Vectorization.
Classification: 11.5.

Nature of problem:
The dynamical triangulated random surface with extrinsic curvature is investigated, with emphasis on its string tension.

Solution method:
The program STRTEN performs a Monte Carlo simulation of the model. The dynamical nature of the triangulation restricts the possiblities to vectorize such a program. In STRTEN vectorization is achieved by simulating a number of independent systems in parallel, a method first described in Ref. [1]. In this way we obtain a speedup factor of 6 between vector and scalar mode. The string tension is extracted by using the method in Ref. [2]. This means that we consider systems with the topology of a torus and with twisted boundary conditions in the embedding space. For a fixed number of points in the triangulation, the following quantities are measured:
  • The mean value of the gaussian part of the action.
  • The mean area of a triangle in the triangulation.
  • The mean value of the extrinsic curvature part of the action, which is taken to be the sum of the cosines of the angles between the normals to two neighbouring triangles.
  • The mean extent of the surface.
  • The susceptibility.
The string tension is obtained from the gaussian term. The embedding space is assumed to be d = 3-dimensional, but the modifications required for arbitrary d are moderate.

Running time:
The time required for an attempt to update three links and the coordinates at one vertex is 17.2 mu seconds. The time needed for measurements is negligible.

References:
[1] J. Ambjorn, D.Boulatov and V.A. Kazakov, Mod. Phys. Lett. A5 (1990) 771.
[2] J. Ambjorn, J.Jurkiewicz, S.Varsted, A.Irback and B.Petersson, "Critical properties of the dynamical random surface with extrinsic curvature", preprint NBI-HE-91-14, May 1991.