Phase structure of four-dimensional gonihedric spin system

We perform Monte Carlo simulations of a gauge invariant spin system which describes random surfaces with gonihedric action in four dimensions. The Hamiltonian is a mixture of one-plaquette and additional two- and three-plaquette interaction terms with specially adjusted coupling constants [G.K. Savvidy, F.J. Wegner, Nucl. Phys. B 413 (1994) 605, G.K. Savvidy, K.G. Savvidy, Phys. Lett. B 324 (1994) 72] For the system with the large self-intersection coupling constant k we observe the second-order phase transition at temperature βc ∼- 1.75. The string tension is generated by quantum fluctuations as it was expected theoretically [G.K. Savvidy, K.G. Savvidy, Mod. Phys. Lett. A 8 (1993) 2963]. This result suggests the existence of a noncritical string in four dimensions. For smaller values of k the system undergoes the first order phase transition and for k close to zero exhibits a smooth crossover.