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

Pierre Le Doussal·Kay Joerg Wiese
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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.

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Pierre Le Doussal, Kay Joerg Wiese. 2005-10-28. Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension. https://doi.org/10.1103/physrevlett.96.197202

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