The Phase Diagram of the Gonihedric 3d Ising Model via CVM

Details The Phase Diagram of the Gonihedric 3d Ising Model via CVM The Phase Diagram of the Gonihedric 3d Ising Model via CVM

1996-07-30

arxiv.org/abs/hep-lat/9607078v1

Phys. Lett. A226, 59-64 (1997)

Physics

High Energy Physics

High Energy Physics - Lattice

8 pages text (LaTex) + 3 eps figures bundled together with uufiles

Scientific paper

10.1016/S0375-9601(96)00918-8

We use the cluster variation method (CVM) to investigate the phase structure of the 3d gonihedric Ising actions defined by Savvidy and Wegner. The geometrical spin cluster boundaries in these systems serve as models for the string worldsheets of the gonihedric string embedded in ${\bf Z}^3$. The models are interesting from the statistical mechanical point of view because they have a vanishing bare surface tension. As a result the action depends only on the angles of the discrete surface and not on the area, which is the antithesis of the standard 3d Ising model. The results obtained with the CVM are in good agreement with Monte Carlo simulations for the critical temperatures and the order of the transition as the self-avoidance coupling $\kappa$ is varied. The value of the magnetization critical exponent $\beta = 0.062 \pm 0.003$, calculated with the cluster variation--Pad\`e approximant method, is also close to the simulation results.

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