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Multicriticality of the gonihedric model in 2+1 dimensions is investigatednumerically. The gonihedric model is a fully frustrated Ising magnet with thefinely tuned plaquette-type (four-body and plaquette-diagonal) interactions,which cancel out the domain-wall surface tension. Because thequantum-mechanical fluctuation along the imaginary-time direction is simplyferromagnetic, the criticality of the (2+1)-dimensional gonihedric model shouldbe an anisotropic one; that is, the respective critical indices of real-space(\perp) and imaginary-time (\parallel) sectors do not coincide. Extending theparameter space to control the domain-wall surface tension, we analyze thecriticality in terms of the crossover (multicritical) scaling theory. By meansof the numerical diagonalization for the clusters with N\le 28 spins, weobtained the correlation-length critical indices(\nu_\perp,\nu_\parallel)=(0.45(10),1.04(27)), and the crossover exponent\phi=0.7(2). Our results are comparable to(\nu_{\perp},\nu_{\parallel})=(0.482,1.230), and \phi=0.688 obtained by Diehland Shpot for the (d,m)=(3,2) Lifshitz point with the \epsilon-expansion methodup to O(\epsilon^2).

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