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

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 d(LC) = 4 the infinite models undergo a paramagnetic-ferromagnetic transition for N > N(c) (N(c) = 2.835 for the random field and N(c) =9.441 for random anisotropy). For N < N(c) and d < d(LC) 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 > d(LC) and the long-range behavior of spin correlations near the surface in the quasi-long-range-order phase for d < d(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, amorphous magnets, and (3)He-A in aerogel.