DOI: 10.1063/1.330232. Finite-size scaling and phenomenological renormalization (invited)

Finite-size scaling and phenomenological renormalization (invited)

10.1063/1.330232

Crossref journal-article

AIP Publishing

Journal of Applied Physics (317)

Abstract

Research in recent years has shown that combining finite-size scaling theory with the transfer matrix technique yields a powerful tool for the investigation of critical behavior. In particular, the method has been used to study two-dimensional statistical mechanical and one-dimensional quantum mechanical systems. We review finite-size scaling theory from the general point of view of renormalization group theory for both continuous and first-order transitions (both for systems with discrete and continuous symmetries). We review applications where a comparison with exact results can be made. These include the Ising, Baxter, and q-state Potts models and the Ising model with a defect line. Various other applications such as quantum systems, the self-avoiding random walk, percolation, and Kosterlitz-Thouless transitions are briefly reviewed. The Kosterlitz-Thouless transitions and the critical fan in the antiferromagnetic 3-state Potts model are discussed at somewhat greater length.

Bibliography

Nightingale, P. (1982). Finite-size scaling and phenomenological renormalization (invited). Journal of Applied Physics, 53(11), 7927â7932.

Authors 1

Peter Nightingale (first)

References 59 Referenced 241

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Dates

Type	When
Created	22 years, 6 months ago (Feb. 14, 2003, 6:21 p.m.)
Deposited	1 year, 6 months ago (Feb. 4, 2024, 8:30 p.m.)
Indexed	3 weeks, 2 days ago (Aug. 2, 2025, 1:26 a.m.)
Issued	42 years, 9 months ago (Nov. 1, 1982)
Published	42 years, 9 months ago (Nov. 1, 1982)
Published Print	42 years, 9 months ago (Nov. 1, 1982)

Funders 0

None

BibTeX

@article{Nightingale_1982, title={Finite-size scaling and phenomenological renormalization (invited)}, volume={53}, ISSN={1089-7550}, url={http://dx.doi.org/10.1063/1.330232}, DOI={10.1063/1.330232}, number={11}, journal={Journal of Applied Physics}, publisher={AIP Publishing}, author={Nightingale, Peter}, year={1982}, month=nov, pages={7927–7932} }

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