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Progress of Theoretical Physics

Higher Order Calculations for d-Dimensional Lattice with d'-Dimensional Defect

R. Abe, K. Yamamoto, K. Ideura

Published Feb 1, 1983• 3 citations
Publisher

Abstract

By means of 1/n expansion, the n-vector model in a d-dimensional lattice is studied where a d′-dimensional defect exists. Previous theories which dealt with the n→∞ limit are extended up to the order λ/n (λ: a parameter specifying the strength of defect). The pair correlation function in the defect space is discussed for the three-dimensional lattice. A critical exponent η// pertaining to the critical correlation is calculated up to the same order.

DOI
10.1143/ptp.69.464

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Progress of Theoretical Physics•Jan 1, 1984•1 citation
By means of 1/n expansion, the n-vector model in a d-dimensional lattice is studied where a d′-dimensional defect exists. Previous theories which dealt with the n→∞ limit are extended up to the order λ/n (λ: a parameter specifying the strength of defect). The pair correlation function in the defect space is discussed for the three-dimensional lattice. A critical exponent η// pertaining to the critical correlation is calculated up to the same order.
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 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 .