Random-field spin models beyond 1 loop: a mechanism for decreasing the lower critical dimension.
The functional renormalization group for the random-field and random-anisotropy O(N) sigma models is studied to 2 loop. The ferromagnetic-disordered (F-D) transition fixed point is found to next order in d = 4 + epsilon for N > N(c) (N(c) = 2.834 740 8 for random field, N(c) = 9.441 21 for random anisotropy). For N < N(c) the lower critical dimension d = d(lc) plunges below d(lc) = 4: we find two fixed points, one describing the quasiordered phase, the other is novel and describes the F-D transition. d(lc) can be obtained in an (N(c)-N) expansion. The theory is also analyzed at large N and a glassy regime is found.
Le Doussal
Pierre
P
CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, Paris, France.
Wiese
Kay Jörg
KJ