Self-avoiding walks in four dimensions: Logarithmic corrections to scaling

D. C. Rapaport

doi:10.1103/physrevb.30.2906

Self-avoiding walks in four dimensions: Logarithmic corrections to scaling

D. C. Rapaport

Department of Physics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Monte Carlo techniques are used to study the conformational properties of self-avoiding walks on the four-dimensional cubic lattice. Both the mean-square end-to-end distance and radius of gyration are found to diverge as N(lnN)q, where N is the number of steps in the walk. The results suggest a value q0.31, whereas the renormalization-group prediction is q=0.375; this small discrepancy is attributable to slowly decaying correction terms.

Original language	English
Pages (from-to)	2906-2908
Number of pages	3
Journal	Physical Review B
Volume	30
Issue number	5
DOIs	https://doi.org/10.1103/physrevb.30.2906
State	Published - 1984

Bibliographical note

Funding Information:
Dr. Hideki Ishii received lecture fees from Astellas Pharma Inc., Daiichi Sankyo Co., Ltd., and Otsuka Pharma Inc. Dr. Toyoaki Murohara received lecture fees from Bayel Pharmaceutical Co., Ltd., Daiichi Sankyo Co., Ltd., Dainippon Sumitomo Pharma Co., Ltd., Kowa Co., Ltd., MSD K.K., Mitsubishi Tanabe Pharma Co., Nippon Boehringer Ingelheim Co., Ltd., Novartis Pharma K.K., Pfizer Japan Inc., Sanofi-aventis K.K., and Takeda Pharmaceutical Co., Ltd. Dr. Toyoaki Murohara received unrestricted research grant for Department of Cardiology, Nagoya University Graduate School of Medicine from Astellas Pharma Inc, Daiichi Sankyo Co., Ltd., Dainippon Sumitomo Pharma Co., Ltd., Kowa Co., Ltd., MSD K.K., Mitsubishi Tanabe Pharma Co., Nippon Boehringer Ingelheim Co., Ltd., Novartis Pharma K.K., Otsuka Pharma Ltd., Pfizer Japan Inc., Sanofi-aventis K.K., Takeda Pharmaceutical Co., Ltd., Teijin Pharma Ltd.

Funding

Dr. Hideki Ishii received lecture fees from Astellas Pharma Inc., Daiichi Sankyo Co., Ltd., and Otsuka Pharma Inc. Dr. Toyoaki Murohara received lecture fees from Bayel Pharmaceutical Co., Ltd., Daiichi Sankyo Co., Ltd., Dainippon Sumitomo Pharma Co., Ltd., Kowa Co., Ltd., MSD K.K., Mitsubishi Tanabe Pharma Co., Nippon Boehringer Ingelheim Co., Ltd., Novartis Pharma K.K., Pfizer Japan Inc., Sanofi-aventis K.K., and Takeda Pharmaceutical Co., Ltd. Dr. Toyoaki Murohara received unrestricted research grant for Department of Cardiology, Nagoya University Graduate School of Medicine from Astellas Pharma Inc, Daiichi Sankyo Co., Ltd., Dainippon Sumitomo Pharma Co., Ltd., Kowa Co., Ltd., MSD K.K., Mitsubishi Tanabe Pharma Co., Nippon Boehringer Ingelheim Co., Ltd., Novartis Pharma K.K., Otsuka Pharma Ltd., Pfizer Japan Inc., Sanofi-aventis K.K., Takeda Pharmaceutical Co., Ltd., Teijin Pharma Ltd.

Funders	Funder number
Kowa Co., Ltd.
Novartis Pharma K.K.
Otsuka Pharma Ltd.
Sanofi-aventis K.K.
Teijin Pharma Ltd
Takeda Pharmaceutical Company
Pfizer Japan
MSD K.K.
Boehringer Ingelheim Japan
Daiichi Sankyo Company
Dainippon Sumitomo Pharma
Astellas Pharma
Mitsubishi Tanabe Pharma Corporation

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title = "Self-avoiding walks in four dimensions: Logarithmic corrections to scaling",

abstract = "Monte Carlo techniques are used to study the conformational properties of self-avoiding walks on the four-dimensional cubic lattice. Both the mean-square end-to-end distance and radius of gyration are found to diverge as N(lnN)q, where N is the number of steps in the walk. The results suggest a value q0.31, whereas the renormalization-group prediction is q=0.375; this small discrepancy is attributable to slowly decaying correction terms.",

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note = "Funding Information: Dr. Hideki Ishii received lecture fees from Astellas Pharma Inc., Daiichi Sankyo Co., Ltd., and Otsuka Pharma Inc. Dr. Toyoaki Murohara received lecture fees from Bayel Pharmaceutical Co., Ltd., Daiichi Sankyo Co., Ltd., Dainippon Sumitomo Pharma Co., Ltd., Kowa Co., Ltd., MSD K.K., Mitsubishi Tanabe Pharma Co., Nippon Boehringer Ingelheim Co., Ltd., Novartis Pharma K.K., Pfizer Japan Inc., Sanofi-aventis K.K., and Takeda Pharmaceutical Co., Ltd. Dr. Toyoaki Murohara received unrestricted research grant for Department of Cardiology, Nagoya University Graduate School of Medicine from Astellas Pharma Inc, Daiichi Sankyo Co., Ltd., Dainippon Sumitomo Pharma Co., Ltd., Kowa Co., Ltd., MSD K.K., Mitsubishi Tanabe Pharma Co., Nippon Boehringer Ingelheim Co., Ltd., Novartis Pharma K.K., Otsuka Pharma Ltd., Pfizer Japan Inc., Sanofi-aventis K.K., Takeda Pharmaceutical Co., Ltd., Teijin Pharma Ltd.",

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N2 - Monte Carlo techniques are used to study the conformational properties of self-avoiding walks on the four-dimensional cubic lattice. Both the mean-square end-to-end distance and radius of gyration are found to diverge as N(lnN)q, where N is the number of steps in the walk. The results suggest a value q0.31, whereas the renormalization-group prediction is q=0.375; this small discrepancy is attributable to slowly decaying correction terms.

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Self-avoiding walks in four dimensions: Logarithmic corrections to scaling

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