  Decoherence mechanisms in crystals of weakly anisotropic magnetic molecules,
such as V15, are studied. We show that an important decohering factor is the
rapid thermal fluctuation of dipolar interactions between magnetic molecules. A
model is proposed to describe the influence of this source of decoherence.
Based on the exact solution of this model, we show that at relatively high
temperatures, about 0.5 K, the quantum coherence in a V15 molecule is not
suppressed, and, in principle, can be detected experimentally. Therefore, these
molecules may be suitable prototype systems for study of physical processes
taking place in quantum computers.
