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Progress of Theoretical Physics

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

R. Abe

Published Aug 1, 1983• 1 citation
Publisher

Abstract

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.

DOI
10.1143/ptp.70.366

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Journal of Physics A Mathematical and General•Sep 21, 1989•2 citations
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.
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.
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.