  Multicriticality of the gonihedric model in 2+1 dimensions is investigated
numerically. The gonihedric model is a fully frustrated Ising magnet with the
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
(\perp) and imaginary-time (\parallel) 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\le 28 spins, we
obtained 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 Diehl
and Shpot for the (d,m)=(3,2) Lifshitz point with the \epsilon-expansion method
up to O(\epsilon^2).
