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.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.

arXiv:1205.1338Physical Review EAug 27, 20129 citations

Surface critical-behavior of some 2-dimensional lattice models

AL Stella, Carlo Vanderzande

Jul 1, 19900 citations

Effect of randomness on surface critical phenomena by means of the 4-d expansion

Kaoru Ohno, Yutaka Okabe

Journal of Magnetism and Magnetic MaterialsFeb 1, 19920 citations

Boundary critical phenomena of the random transverse Ising model in D≥2 dimensions

István A. Kovács, Ferenc Iglói

Using the strong disorder renormalization group method, we study numerically the critical behavior of the random transverse Ising model at a free surface, at a corner, and at an edge in two-, three-, and four-dimensional lattices. The surface magnetization exponents are found to be ${x}_{s}=1.60(2),$ 2.65(15), and $3.7(1)$ in $D=2,$ 3, and 4, respectively, which do not depend on the form of disorder. We have also studied critical magnetization profiles in slab, pyramid, and wedge geometries with fixed-free boundary conditions and analyzed their scaling behavior.Using the strong disorder renormalization group method, we study numerically the critical behavior of the random transverse Ising model at a free surface, at a corner, and at an edge in two-, three-, and four-dimensional lattices. The surface magnetization exponents are found to be ${x}_{s}=1.60(2),$ 2.65(15), and $3.7(1)$ in $D=2,$ 3, and 4, respectively, which do not depend on the form of disorder. We have also studied critical magnetization profiles in slab, pyramid, and wedge geometries with fixed-free boundary conditions and analyzed their scaling behavior.

arXiv:1211.2623Physical Review BJan 18, 20132 citations

Surface critical behavior of random systems: Ordinary transition

Z. Usatenko, Mykola A. Shpot, Chin‐Kun Hu

We calculate the surface critical exponents of the ordinary transition occurring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation as well as in 4-epsilon dimensions. At d=4-epsilon we extend, up to the next-to-leading order, the previous first-order results of the square root of epsilon expansion by Ohno and Okabe [Phys. Rev. B 46, 5917 (1992)]. In both cases numerical estimates for surface exponents are computed using Padé approximants extrapolating the perturbation theory expansions. The obtained results indicate that the critical behavior of semi-infinite systems with quenched bulk disorder is characterized by the new set of surface critical exponents.We calculate the surface critical exponents of the ordinary transition occurring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation as well as in 4-epsilon dimensions. At d=4-epsilon we extend, up to the next-to-leading order, the previous first-order results of the square root of epsilon expansion by Ohno and Okabe [Phys. Rev. B 46, 5917 (1992)]. In both cases numerical estimates for surface exponents are computed using Padé approximants extrapolating the perturbation theory expansions. The obtained results indicate that the critical behavior of semi-infinite systems with quenched bulk disorder is characterized by the new set of surface critical exponents.

arXiv:cond-mat/0011114Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsApr 11, 200112 citations

Critical behavior of a spherical model with a free surface

Michael N. Barber

Journal of Statistical PhysicsJan 1, 197433 citations

{x}_{s}=1.60(2),

2.65(15), and

3.7(1)

D=2,

3, and 4, respectively, which do not depend on the form of disorder. We have also studied critical magnetization profiles in slab, pyramid, and wedge geometries with fixed-free boundary conditions and analyzed their scaling behavior.