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Random-field and random-anisotropy O(N) spin systems with a free surface

Andrei A. Fedorenko

  • Laboratoire de Physique de l’Ecole Normale Supérieure de Lyon, Unité Mixte de Recherche No. 5672 associée au Centre National de la Recherche Scientifique, 46 Allée d’Italie, 69007 Lyon, France

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Phys. Rev. E 86, 021131 – Published 27 August, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.021131

Abstract

We study the surface scaling behavior of a semi-infinite d-dimensional O(N) spin system in the presence of a quenched random field and random anisotropy disorders. It is known that above the lower critical dimension dLC=4 the infinite models undergo a paramagnetic-ferromagnetic transition for N>Nc (Nc=2.835 for the random field and Nc=9.441 for random anisotropy). For N<Nc and d<dLC there exists a quasi-long-range-order phase with a zero order parameter and a power-law decay of spin correlations. Using a functional renormalization group, we derive the surface scaling laws that describe the ordinary surface transition for d>dLC and the long-range behavior of spin correlations near the surface in the quasi-long-range-order phase for d<dLC. The corresponding surface exponents are calculated to one-loop order. The obtained results can be applied to the surface scaling of periodic elastic systems in disordered media, amorphous magnets, and 3He-A in aerogel.

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Phys. Rev. E 86, 021131– Published 27 August, 2012
  • Received 7 May 2012

©2012 American Physical Society

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