SCALING OF FLUCTUATIONS AND CRITICAL EXPONENTS

We present a new technique to describe the abnormal behavior of certai n fluctuation observables in the critical regime of quantum statistica l systems which undergo a phase transition. The idea is to rescale the local fluctuation operators by a relevant external parameter of the s ystem, in addition to the usual scaling with the inverse square root o f the volume. The scaling indices used in this scaling procedure are d irectly related to the critical exponents. Furthermore, it is explaine d that this new method of scaling preserves the CCR structure of the a lgebra of macroscopic fluctuations. Finally, scaling indices are compu ted for the relevant microscopic observables at all temperatures in a mean field approximation for a quantum anharmonic crystal. These indic es yield the same critical exponents as predicted by mean field theory .