Broidioi M. , Van Canneyt M.
Scaling of Fluctuations and Critical Exponents
(35K, LaTeX)
ABSTRACT. We present a new technique to describe the abnormal
behaviour of certain fluctuation observables in the
critical regime of quantum statistical systems which
undergo a phase transition. The idea is to rescale the
local fluctuation operators by a relevant external
parameter of the system, in addition to the usual scaling
with the inverse square root of the volume. The scaling
indices used in this scaling procedure are directly
related to the critical exponents.
Furthermore, it is explained that this new method of
scaling preserves the CCR structure of the algebra of
macroscopic fluctuations.
Finally, scaling indices are computed for the relevant
microscopic observables at all temperatures in a mean
field approximation for a quantum anharmonic crystal.
These indices yield the same critical exponents as
predicted by mean field theory.