  The critical and multicritical behavior of the simple cubic Ising model with
nearest-neighbor, next-nearest-neighbor and plaquette interactions is studied
using the cube and star-cube approximations of the cluster variation method and
the recently proposed cluster variation--Pad\'e approximant method. Particular
attention is paid to the line of critical end points of the
ferromagnetic-paramagnetic phase transition: its (multi)critical exponents are
calculated, and their values suggest that the transition belongs to a novel
universality class. A rough estimate of the crossover exponent is also given.
