Progress of Theoretical Physics

d'-Dimensional Defect in d-Dimensional Lattice: Nonuniversal Critical Exponents for Long-Range Interactions in the Limit n ->

K. Ideura, R. Abe

Published Jan 1, 1984• 1 citation

Abstract

Local critical exponent η∥ in a defect space is investigated up to O(λ2) in the limit n →∞ for a system with long-range interactions. It is shown that if d=3 σ/ 2 and d' = σ critical exponents are nonuniversal but satisfy usual scaling law relations up to O(λ).

DOI: 10.1143/ptp.71.27

Related papers

d'-Dimensional Defect in d-Dimensional Lattice. III: Perpendicular Correlations in the Limit n->

R. Abe

By extending previous treatments, local critical exponents η⊧, γ⊧ and ν;⊧ defined in a region perpendicular to the defect space are studied in the limit n→∞. Actual calculations are carried out up to O(λ). It is shown that if d’=2η⊧ and γ⊧ are nonuniversal but ν;⊧ is universal. A scaling law relation between η⊧ and η∥ and that among η⊧, γ⊧ and ν;⊧ are discussed.

Progress of Theoretical PhysicsAug 1, 19831 citation

d'-Dimensional Defect in d-Dimensional Lattice. I: --Nonuniversal Local Critical Exponent in the Limit n-> --

R. Abe

The n-vector model in a d-dimensional lattice is studied where a d′-dimensional defect exists. The defect is defined in such a way that the spin length there is different from that in other parts. The pair correlation function in the defect space is discussed in the limit n→∞. It is shown that if d′=2 a critical exponent η• pertaining to the critical correlation is nonuniversal; it does depend on λ where λ is a parameter describing the strength of defect. The η′ is calculated up to order of λ.

Progress of Theoretical PhysicsApr 1, 198111 citations

d'-Dimensional Defect in d-Dimensional Lattice. II: Local Exponents ', ' and ' in the Limit n->

R. Abe

By generalizing a previous treatment, local critical exponents β′, γ′ and ν′ in the defect space are studied in the limit n→∞. Actual calculations are carried out up to the order of λ. It is shown that these exponents satisfy usual scaling law relations up to this order.

Progress of Theoretical PhysicsJun 1, 19819 citations

Two-Dimensional Defect in Three-Dimensional Lattice: -- Local Critical Exponents ', ' and ' in the Limit n -> --

K. Yamamoto, R. Abe

By extending a previous treatment, local critical exponents η′, β′ and ν′ in the defect space are studied up to order λ2 in the limit n → ∞. Actual calculations are carried out for a system where two-dimensional defect exists in three-dimensional lattice. It is proved that the results obtained are consistent with a simple power-law assumption for relevant quantities. It is also shown that these exponents satisfy scaling law relations up to this order.

Progress of Theoretical PhysicsDec 1, 19814 citations

Local magnetisation of the n-vector model with a large-scale defect in the limit n to infinity

R. Z. Bariev, Ilyas Z. Ilaldinov

The local magnetisation of the three-dimensional n-vector model is studied near the large-scale d'-dimensional defect in the limit n to infinity . The model is characterised by the fact that the spin lengths close to the defect are changed as S r 2 =n(1- lambda /r) with the distance r from the defect. It is shown that near the critical point the local magnetisation exhibits a nonuniversal behaviour if d'=0, 1 and a nonscaling behaviour if d'=2. In the first case the critical exponents beta ' and nu ' are calculated up to the order of lambda and it is shown that these exponents satisfy the usual scaling law relations up to this order.

Journal of Physics A Mathematical and GeneralSep 21, 19892 citations

Correlation functions of the n-vector model with a large-scale defect in the limit n to infinity

R. Z. Bariev, Ilyas Z. Ilaldinov

The correlation functions of the three-dimensional n-vector model are studied near the large-scale d'-dimensional defect in the limit n to infinity . The model is characterised by the fact that the spin lengths close to the defect are changed with respect to their bulk value. The deviations decay as - lambda /r with the distance r from the defect. It is shown that at the critical point the correlation function exhibits nonscaling behaviour if d'=2 and nonuniversal behaviour if d'=1. The deviation of a critical exponent eta is calculated up to order of lambda .

Journal of Physics A Mathematical and GeneralSep 21, 19899 citations