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

TL;DR

This paper investigates the surface behavior of semi-infinite disordered O(N) spin systems, deriving surface scaling laws and exponents using functional renormalization group methods, applicable to elastic systems and amorphous magnets.

Contribution

It provides the first derivation of surface scaling laws and exponents for disordered O(N) spin systems with quenched randomness using functional renormalization group techniques.

Findings

Derived surface scaling laws for different phases.

Calculated surface exponents to one-loop order.

Applicable to elastic systems in disordered media.

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 $N<N_c$ and $d<d_{\mathrm{lc}}$ there exists a quasi-long-range ordered phase with zero order parameter and a power-law decay of spin correlations. Using functional renormalization group we derive the surface scaling laws which describe the ordinary surface transition for $d>d_{\mathrm{lc}}$ 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.