  We study the effects of random fluctuations on quantum phase transitions by
the energy gap analysis. For the infinite-ranged spin-glass models with a
transverse field, we find that a strong sample-to-sample fluctuation effect
leads to broad distributions of the energy gap. As a result, the linear,
spin-glass, and nonlinear susceptibilities behave differently from each other.
The power-law tail of the distribution implies a quantum Griffiths-like effect
that could be observed in various random quantum systems. We also discuss the
mechanisms of the phase transition in terms of the energy gap by comparing the
Sherrington-Kirkpatrick model and random energy model, which demonstrate the
difference between the continuous and discontinuous phase transitions.
