Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0306197 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Crossover between special and ordinary transitions in random semi-infinite Ising-like systems

Z. Usatenko, Chin‐Kun Hu

Published Dec 24, 2003• 6 citations
arXivHTMLPDF

Abstract

We consider the crossover behavior between special and ordinary surface transitions in three-dimensional semi-infinite Ising-like systems with random quenched bulk disorder. We calculate the surface crossover critical exponent Phi, the critical exponents of the layer alpha(1), and local specific heats alpha(11) by applying the field theoretic approach directly in three spatial dimensions (d=3) up to the two-loop approximation. The numerical estimates of the resulting two-loop series expansions for the surface critical exponents are computed by means of Padé and Padé-Borel resummation techniques. We find that Phi, alpha(1), alpha(11) obtained in the present paper are different from their counterparts of pure Ising systems. The obtained results support the idea that in a system with random quenched bulk disorder the plane boundary is characterized by a new set of critical exponents.

DOI
10.1103/physreve.68.066115

Related papers

Critical behavior of semi-infinite random systems at the special surface transition

Z. Usatenko, Chin‐Kun Hu

We use a three-dimensional massive field theory up to the two-loop approximation to study the critical behavior of semi-infinite quenched random Ising-like systems at the special surface transition. Besides, we extend up to the next-to leading order, the previous first-order results of the sqrt[epsilon] expansion obtained by Ohno and Okabe [Phys. Rev. B 46, 5917 (1992)]. The numerical estimates for surface critical exponents in both cases are computed by means of the Padé analysis. Moreover, in the case of the massive field theory we perform Padé-Borel resummation of the resulting two-loop series expansions for surface critical exponents. The most reliable estimates for critical exponents of semi-infinite systems with quenched bulk randomness at the special surface transition, which we can obtain in the frames of the present approximation scheme, are eta(//)=-0.238, Delta(1)=1.098, eta( perpendicular )=-0.104, beta(1)=0.258, gamma(11)=0.839, gamma(1)=1.426, delta(1)=6.521, and delta(11)=4.249. These values are different from critical exponents for pure semi-infinite Ising-like systems and show that in a system with quenched bulk randomness the plane boundary is characterized by a new set of critical exponents at the special surface transition.

arXiv:cond-mat/0105184•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jun 13, 2002•9 citations

Investigation of surface critical behavior of semi-infinite systems with cubic anisotropy

Z. Usatenko

The critical behavior at the special surface transition and crossover bevavior from special to ordinary surface transition in semi-infinite n-component anisotropic cubic models are investigated by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation. The crossover behavior for random semi-infinite Ising-like system, which is the nontrivial particular case of the cubic model in the limit $n\to 0$, is also investigated. The numerical estimates of the resulting two-loop series expansions for the critical exponents of the special surface transition, surface crossover critical exponent $Φ$ and the surface critical exponents of the layer, $α_{1}$, and local specific heats, $α_{11}$, are computed by means of Pade and Pade-Borel resummation techniques. For $nn_{c}$ the cubic fixed point is stable, where $n_{c}$ is the marginal spin dimensionality of the cubic model. The obtained results indicate that the surface critical behavior of semi-infinite systems with cubic anisotropy is characterized by new set of surface critical exponents for $n>n_{c}$.

arXiv:cond-mat/0211654•Nov 28, 2002•0 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.

arXiv:cond-mat/0011114•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Apr 11, 2001•12 citations

Critical behavior of disordered systems with a free surface

С. В. Белим

The behavior of homogeneous and disordered systems with a free boundary is described on the basis of group theory in the two-loop approximation directly in three-dimensional space. The effect of the free boundary on the regime of the bulk critical behavior is revealed. It is shown that the boundedness of the system slightly affects the regime of the bulk critical behavior in the case of the ordinary transition, whereas this effect is more noticeable in the case of the special transition. Surface critical phenomena are described for homogeneous and disordered systems, and the critical exponents are calculated in the two-loop approximation. It is shown that the effect of impurities is insignificant in the special phase transition, whereas it is more noticeable in the ordinary phase transition. The derived critical exponents are compared with the computer-simulation results.

Journal of Experimental and Theoretical Physics•Oct 1, 2006•11 citations

Surface criticality in random field magnets

Lasse Laurson, Mikko J. Alava

The boundary-induced scaling of three-dimensional random field Ising magnets is investigated close to the bulk critical point by exact combinatorial optimization methods. We measure several exponents describing surface criticality: ${\ensuremath{\beta}}_{1}$ for the surface layer magnetization and the surface excess exponents for the magnetization and the specific heat, ${\ensuremath{\beta}}_{s}$ and ${\ensuremath{\alpha}}_{s}$. The latter are related to the bulk phase transition by the same scaling laws as in pure systems, but only with the same violation of the hyperscaling exponent $\ensuremath{\theta}$ as in the bulk. The boundary disorders faster than the bulk, and the experimental and theoretical implications are discussed.

arXiv:cond-mat/0510727•Physical Review B•Dec 9, 2005•3 citations

Surface critical behaviour of semi-infinite systems with cubic anisotropy at the ordinary transition

Z Usatenko, Józef Spałek

The critical behaviour at the ordinary transition in semi-infinite n -component anisotropic cubic models is investigated by applying the field theoretic approach in d = 3 dimensions up to the two-loop approximation. Numerical estimates of the resulting two-loop series expansions for the critical exponents of the ordinary transition are computed by means of Padé resummation techniques. For n < n c the system belongs to the universality class of the isotropic n -component model, while for n > n c the cubic fixed point becomes stable, where n c < 3 is the marginal spin dimensionality of the cubic model. The obtained results indicate that the surface critical behaviour of the semi-infinite systems with cubic anisotropy is characterized by a new set of surface critical exponents for n > n c .

arXiv:cond-mat/0312320•Journal of Physics A Mathematical and General•Jul 1, 2004•3 citations
We consider the crossover behavior between special and ordinary surface transitions in three-dimensional semi-infinite Ising-like systems with random quenched bulk disorder. We calculate the surface crossover critical exponent Phi, the critical exponents of the layer alpha(1), and local specific heats alpha(11) by applying the field theoretic approach directly in three spatial dimensions (d=3) up to the two-loop approximation. The numerical estimates of the resulting two-loop series expansions for the surface critical exponents are computed by means of Padé and Padé-Borel resummation techniques. We find that Phi, alpha(1), alpha(11) obtained in the present paper are different from their counterparts of pure Ising systems. The obtained results support the idea that in a system with random quenched bulk disorder the plane boundary is characterized by a new set of critical exponents.
We use a three-dimensional massive field theory up to the two-loop approximation to study the critical behavior of semi-infinite quenched random Ising-like systems at the special surface transition. Besides, we extend up to the next-to leading order, the previous first-order results of the sqrt[epsilon] expansion obtained by Ohno and Okabe [Phys. Rev. B 46, 5917 (1992)]. The numerical estimates for surface critical exponents in both cases are computed by means of the Padé analysis. Moreover, in the case of the massive field theory we perform Padé-Borel resummation of the resulting two-loop series expansions for surface critical exponents. The most reliable estimates for critical exponents of semi-infinite systems with quenched bulk randomness at the special surface transition, which we can obtain in the frames of the present approximation scheme, are eta(//)=-0.238, Delta(1)=1.098, eta( perpendicular )=-0.104, beta(1)=0.258, gamma(11)=0.839, gamma(1)=1.426, delta(1)=6.521, and delta(11)=4.249. These values are different from critical exponents for pure semi-infinite Ising-like systems and show that in a system with quenched bulk randomness the plane boundary is characterized by a new set of critical exponents at the special surface transition.
The critical behavior at the special surface transition and crossover bevavior from special to ordinary surface transition in semi-infinite n-component anisotropic cubic models are investigated by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation. The crossover behavior for random semi-infinite Ising-like system, which is the nontrivial particular case of the cubic model in the limit n→0n\to 0n→0, is also investigated. The numerical estimates of the resulting two-loop series expansions for the critical exponents of the special surface transition, surface crossover critical exponent ΦΦΦ and the surface critical exponents of the layer, α1α_{1}α1​, and local specific heats, α11α_{11}α11​, are computed by means of Pade and Pade-Borel resummation techniques. For nncnn_{c}nnc​ the cubic fixed point is stable, where ncn_{c}nc​ is the marginal spin dimensionality of the cubic model. The obtained results indicate that the surface critical behavior of semi-infinite systems with cubic anisotropy is characterized by new set of surface critical exponents for n>ncn>n_{c}n>nc​.
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.
The behavior of homogeneous and disordered systems with a free boundary is described on the basis of group theory in the two-loop approximation directly in three-dimensional space. The effect of the free boundary on the regime of the bulk critical behavior is revealed. It is shown that the boundedness of the system slightly affects the regime of the bulk critical behavior in the case of the ordinary transition, whereas this effect is more noticeable in the case of the special transition. Surface critical phenomena are described for homogeneous and disordered systems, and the critical exponents are calculated in the two-loop approximation. It is shown that the effect of impurities is insignificant in the special phase transition, whereas it is more noticeable in the ordinary phase transition. The derived critical exponents are compared with the computer-simulation results.
The boundary-induced scaling of three-dimensional random field Ising magnets is investigated close to the bulk critical point by exact combinatorial optimization methods. We measure several exponents describing surface criticality: ${\ensuremath{\beta}}_{1}$ for the surface layer magnetization and the surface excess exponents for the magnetization and the specific heat, ${\ensuremath{\beta}}_{s}$ and ${\ensuremath{\alpha}}_{s}$. The latter are related to the bulk phase transition by the same scaling laws as in pure systems, but only with the same violation of the hyperscaling exponent $\ensuremath{\theta}$ as in the bulk. The boundary disorders faster than the bulk, and the experimental and theoretical implications are discussed.
The critical behaviour at the ordinary transition in semi-infinite n -component anisotropic cubic models is investigated by applying the field theoretic approach in d = 3 dimensions up to the two-loop approximation. Numerical estimates of the resulting two-loop series expansions for the critical exponents of the ordinary transition are computed by means of Padé resummation techniques. For n < n c the system belongs to the universality class of the isotropic n -component model, while for n > n c the cubic fixed point becomes stable, where n c < 3 is the marginal spin dimensionality of the cubic model. The obtained results indicate that the surface critical behaviour of the semi-infinite systems with cubic anisotropy is characterized by a new set of surface critical exponents for n > n c .