Two and Three-Dimensional Spin Systems with Gonihedric Action

Abstract

We perform numerical simulations of the two and three-dimensional spin systems with competing interaction. They describe the model of random surfaces with linear-gonihedric action.The degeneracy of the vacuum state of this spin system is equal to $d\cdot 2^N$ for the lattice of the size $N^d$. We observe the second order phase transition of the three-dimensional system, at temperature ${\beta }_c\simeq 0.43932$ which almost coincides with ${\beta }_c$ of the 2D Ising model. This confirms the earlier analytical result for the case when self-interaction coupling constant $k$ is equal to zero. We suggest the full set of order parameters which characterize the structure of the vacuum states and of the phase transition.

10 pages,Latex,The figures are available

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