Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension

Details Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension

2005-10-13

arxiv.org/abs/cond-mat/0510344v3

Phys. Rev. Let. 96 (2006) 197202

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.96.197202

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.

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