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arXiv · 1205.1338

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

Andrei A. Fedorenko
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Abstract

We study the surface scaling behavior of a semi-infinite $d$-dimensional O(N) spin system in the presence of quenched random field and random anisotropy disorders. It is known that above the lower critical dimension $d_{\mathrm{lc}}=4$ the infinite models undergo a paramagnetic-ferromagnetic transition for $N>N_c$ ($N_c=2.835$ for random field and $N_c=9.441$ for random anisotropy). For $N d_{\mathrm{lc}}$ and the long-range behavior of spin correlations near the surface in the quasi-long-range ordered phase for $d<d_{\mathrm{lc}}$. 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 and amorphous magnets.

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Andrei A. Fedorenko. 2012-05-07. Random field and random anisotropy O(N) spin systems with a free surface. https://doi.org/10.1103/physreve.86.021131

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