Random field spin models beyond one
loop: a mechanism for decreasing the lower critical dimension
Pierre Le Doussal, Kay Jörg Wiese
CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France
Abstract
The functional RG for the random field and
random anisotropy O(N) sigma-models is studied to two
loop. The ferromagnetic/disordered (F/D) transition fixed point is
found to next order in d=4+ε for N >
Nc (Nc=2.8347408 for random field,
Nc=9.44121 for random anisotropy). For N <
Nc the lower critical dimension
d=dlc plunges below dlc=4:
we find two fixed points, one describing the quasi-ordered
phase, the other is novel and describes the F/D transition.
dlc can be obtained in an
(Nc-N)-expansion. The theory is also
analyzed at large N and a non-trivial glass fixed point is
found, at variance with recent claims.
cond-mat/0510344 [pdf]
Phys. Rev. Lett. 96 (2006) 197202
[pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.