Multicriticality of the(2+1)-dimensional gonihedric model: A realization of the(d,m)=(3,2)Lifshitz point

Abstract

Multicriticality of the gonihedric model in 2+1 dimensions is investigated numerically. The gonihedric model is a fully frustrated Ising magnet with finely tuned plaquette-type (four-body and plaquette-diagonal) interactions, which cancel out the domain-wall surface tension. Because the quantum-mechanical fluctuation along the imaginary-time direction is simply ferromagnetic, the criticality of the (2+1) -dimensional gonihedric model should be an anisotropic one; that is, the respective critical indices of real-space (perpendicular) and imaginary-time (||) sectors do not coincide. Extending the parameter space to control the domain-wall surface tension, we analyze the criticality in terms of the crossover (multicritical) scaling theory. By means of the numerical diagonalization for the clusters with N< or =28 spins, we obtained the correlation-length critical indices (nu{perpendicular},nu{||})=[0.45(10),1.04(27)] , and the crossover exponent phi=0.7(2) . Our results are comparable to (nu{perpendicular},nu{||})=(0.482,1.230) , and phi=0.688 obtained by Diehl and Shpot for the (d,m)=(3,2) Lifshitz point with the epsilon-expansion method up to O(epsilon{2}) .