Effects of a random magnetic field on the phase transition of the spherical model in d space-dimensions are investigated by n->0 technique of the n-times replicated Hamiltonian.The critical temperature T, (fl.o, d) as a function of the strength fl.o of the radom field and the space dimensions d is obtained.It is shown that any critical exponent of this system is equal to that of (d-2)-dimensional pure system for sufficiently close to T,.The crossover effect from d-dimensional behavior to (d-2)-dimensional behavior is discussed.The equation of state and the universal amplitude are also obtained.
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Fumihiko Tanaka (1977) studied this question.