Three-dimensional gonihedric spin system

Abstract

We perform Monte Carlo simulations of a three-dimensional spin system with a Hamiltonian which contains only four-spin interaction term. This system describes random surfaces with extrinsic curvature - gonihedric action. We study the anisotropic model when the coupling constants ${\beta }_S$ for the space-like plaquettes and ${\beta }_T$ for the transverse-like plaquettes are different. In the two limits ${\beta }_S=0$ and ${\beta }_T=0$ the system has been solved exactly and the main interest is to see what happens when we move away from these points towards the isotropic point, where we recover the original model. We find that the phase transition is of first order for ${\beta }_T={\beta }_S\approx 0.25,$ while away from this point it becomes weaker and eventually turns to a crossover. The conclusion which can be drown from this result is that the exact solution at the point ${\beta }_S=0$ in terms of 2d-Ising model should be considered as a good zero order approximation in the description of the system also at the isotropic point ${\beta }_S={\beta }_T$ and clearly confirms the earlier findings that at the isotropic point the original model shows a first order phase transition.

11 pages, 10 figures, shortened version

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