  Three-dimensional Ising model with the plaquette-type (next-nearest-neighbor
and four-spin) interactions is investigated numerically. This extended Ising
model, the so-called gonihedric model, was introduced by Savvidy and Wegner as
a discretized version of the interacting (closed) surfaces without surface
tension. The gonihedric model is notorious for its slow relaxation to the
thermal equilibrium (glassy behavior), which deteriorate the efficiency of the
Monte Carlo sampling. We employ the transfer-matrix (TM) method, implementing
Novotny's idea, which enables us to treat arbitrary number of spins $N$ for one
TM slice even in three dimensions. This arbitrariness admits systematic
finite-size-scaling analyses. Accepting the extended parameter space by Cirillo
and co-worker, we analyzed the (multi) criticality of the gonihedric model for
N \le 13. Thereby, we found that, as first noted by Cirillo and co-worker
analytically (cluster-variation method), the data are well described by the
multi-critical (crossover) scaling theory. That is, the previously reported
nonstandard criticality for the gonihedric model is reconciled with a crossover
exponent and the ordinary three-dimensional-Ising universality class. We
estimate the crossover exponent and the correlation-length critical exponent at
the multi-critical point as \phi=0.6(2) and \nu=0.45(15), respectively.
