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

Multicriticality of the three-dimensional Ising model with plaquette interactions: An extension of Novotny’s transfer-matrix formalism