Replica-space renormalization in random-field systems

Conference · Tue Jan 01 04:00:00 EST 1985

OSTI ID:5666064

Shapir, Y

The critical behavior of random-field systems is characterized by exponentially long relaxation times. They may differ by orders of magnitude and slow modes have to be considered quenched with respect to the faster ones. This requires a drastic modification of the renormalization process in which the degrees of freedom are integrated out. A new replica-space renormalization procedure, to carry out the coarse-graining of the time intervals, is presented. We relate by recursion-relations the effective reduced dimensions of consecutive time scales. Their stable fixed-points yield the apparent dimensionalities for the longest and shortest time scales, which are insensitive to the exact behavior on intermediate scales. For Ising systems we find that d = 2 is the lower critical dimension in both regimes. The thermal exponents for d = 3, in the short-time observable regime, are related to those of the pure system in d = 2. This is consistent with the observations in field-cooled random antiferromagnets of the correlation length exponent nu approx. = 1 (by neutron scattering) and of the symmetric logarithmic divergence in the specific-heat (by linear birefringence). 17 refs., 3 figs.

• Research Organization: Brookhaven National Lab., Upton, NY (USA)
• DOE Contract Number: AC02-76CH00016
• OSTI ID: 5666064
• Report Number(s): BNL-36708; CONF-850890-3; ON: DE85014800
• Country of Publication: United States
• Language: English

Related Subjects

656000* -- Condensed Matter Physics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CRYSTAL MODELS
ELECTROMAGNETIC FIELDS
ISING MODEL
MATHEMATICAL MODELS
RECURSION RELATIONS
RENORMALIZATION