Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension
Disordered Systems and Neural Networks
2009-11-11 v3 Statistical Mechanics
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+epsilon for N > N_c (N_c=2.8347408 for random field, N_c=9.44121 for random anisotropy). For N < N_c the lower critical dimension plunges below d=4: we find two fixed points, one describing the quasi-ordered phase, the other is novel and describes the F/D transition. The lower critical dimension can be obtained in an (N_c-N)-expansion. The theory is also analyzed at large N and a glassy regime is found.
Cite
@article{arxiv.cond-mat/0510344,
title = {Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension},
author = {Pierre Le Doussal and Kay Joerg Wiese},
journal= {arXiv preprint arXiv:cond-mat/0510344},
year = {2009}
}
Comments
4 pages, 5 figures