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Fractal dimension of critical curves in the O(n) -symmetric φ4 model and crossover exponent at 6-loop order : Loop-erased random walks, self-avoiding walks, Ising, XY, and Heisenberg models. / Kompaniets, Mikhail; Wiese, Kay Jörg.

в: Physical Review E, Том 101, № 1, 012104, 03.01.2020.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Kompaniets, M & Wiese, KJ 2020, 'Fractal dimension of critical curves in the O(n) -symmetric φ4 model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY, and Heisenberg models', Physical Review E, Том. 101, № 1, 012104. https://doi.org/10.1103/PhysRevE.101.012104

APA

Kompaniets, M., & Wiese, K. J. (2020). Fractal dimension of critical curves in the O(n) -symmetric φ4 model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY, and Heisenberg models. Physical Review E, 101(1), [012104]. https://doi.org/10.1103/PhysRevE.101.012104

Vancouver

Kompaniets M, Wiese KJ. Fractal dimension of critical curves in the O(n) -symmetric φ4 model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY, and Heisenberg models. Physical Review E. 2020 Янв. 3;101(1). 012104. https://doi.org/10.1103/PhysRevE.101.012104

Author

Kompaniets, Mikhail ; Wiese, Kay Jörg. / Fractal dimension of critical curves in the O(n) -symmetric φ4 model and crossover exponent at 6-loop order : Loop-erased random walks, self-avoiding walks, Ising, XY, and Heisenberg models. в: Physical Review E. 2020 ; Том 101, № 1.

BibTeX

@article{b12a7d02aeb64912adf8d0021663e402,
title = "Fractal dimension of critical curves in the O(n) -symmetric φ4 model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY, and Heisenberg models",
abstract = "We calculate the fractal dimension df of critical curves in the O(n)-symmetric (φ- 2)2 theory in d=4-ϵ dimensions at 6-loop order. This gives the fractal dimension of loop-erased random walks at n=-2, self-avoiding walks (n=0), Ising lines (n=1), and XY lines (n=2), in agreement with numerical simulations. It can be compared to the fractal dimension dftot of all lines, i.e., backbone plus the surrounding loops, identical to dftot=1/ν. The combination φc=df/dftot=νdf is the crossover exponent, describing a system with mass anisotropy. Introducing a self-consistent resummation procedure and combining it with analytic results in d=2 allows us to give improved estimates in d=3 for all relevant exponents at 6-loop order.",
author = "Mikhail Kompaniets and Wiese, {Kay J{\"o}rg}",
note = "Funding Information: We thank A. A. Fedorenko for insightful discussions. The work of M.K. was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (Grant No. 18-1-2-43-1). M.K. thanks Laboratoire de physique de l'ENS (LPENS) for hospitality during the work on this paper. Publisher Copyright: {\textcopyright} 2020 American Physical Society. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = jan,
day = "3",
doi = "10.1103/PhysRevE.101.012104",
language = "English",
volume = "101",
journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",
issn = "1539-3755",
publisher = "American Physical Society",
number = "1",

}

RIS

TY - JOUR

T1 - Fractal dimension of critical curves in the O(n) -symmetric φ4 model and crossover exponent at 6-loop order

T2 - Loop-erased random walks, self-avoiding walks, Ising, XY, and Heisenberg models

AU - Kompaniets, Mikhail

AU - Wiese, Kay Jörg

N1 - Funding Information: We thank A. A. Fedorenko for insightful discussions. The work of M.K. was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (Grant No. 18-1-2-43-1). M.K. thanks Laboratoire de physique de l'ENS (LPENS) for hospitality during the work on this paper. Publisher Copyright: © 2020 American Physical Society. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/1/3

Y1 - 2020/1/3

N2 - We calculate the fractal dimension df of critical curves in the O(n)-symmetric (φ- 2)2 theory in d=4-ϵ dimensions at 6-loop order. This gives the fractal dimension of loop-erased random walks at n=-2, self-avoiding walks (n=0), Ising lines (n=1), and XY lines (n=2), in agreement with numerical simulations. It can be compared to the fractal dimension dftot of all lines, i.e., backbone plus the surrounding loops, identical to dftot=1/ν. The combination φc=df/dftot=νdf is the crossover exponent, describing a system with mass anisotropy. Introducing a self-consistent resummation procedure and combining it with analytic results in d=2 allows us to give improved estimates in d=3 for all relevant exponents at 6-loop order.

AB - We calculate the fractal dimension df of critical curves in the O(n)-symmetric (φ- 2)2 theory in d=4-ϵ dimensions at 6-loop order. This gives the fractal dimension of loop-erased random walks at n=-2, self-avoiding walks (n=0), Ising lines (n=1), and XY lines (n=2), in agreement with numerical simulations. It can be compared to the fractal dimension dftot of all lines, i.e., backbone plus the surrounding loops, identical to dftot=1/ν. The combination φc=df/dftot=νdf is the crossover exponent, describing a system with mass anisotropy. Introducing a self-consistent resummation procedure and combining it with analytic results in d=2 allows us to give improved estimates in d=3 for all relevant exponents at 6-loop order.

UR - http://www.scopus.com/inward/record.url?scp=85078099628&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.101.012104

DO - 10.1103/PhysRevE.101.012104

M3 - Article

C2 - 32069567

AN - SCOPUS:85078099628

VL - 101

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 1

M1 - 012104

ER -

ID: 73725547