Finite-size scaling of correlation functions in finite systems

Xin Zhang; Gao Ke Hu; Yong Wen Zhang; Xiao Teng Li; Xiao Song Chen

doi:10.1007/s11433-018-9266-x

Finite-size scaling of correlation functions in finite systems

Xin Zhang, Gao Ke Hu, Yong Wen Zhang, Xiao Teng Li, Xiao Song Chen

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

9 Scopus citations

Abstract

We propose the finite-size scaling of correlation functions in finite systems near their critical points. At a distance r in a d-dimensional finite system of size L, the correlation function can be written as the product of |r|^{−(d−2+η)} and a finite-size scaling function of the variables r/L and tL^1/v, where t = (T − T_c)=T_c, η is the critical exponent of correlation function, and v is the critical exponent of correlation length. The correlation function only has a sigificant directional dependence when |r| is compariable to L. We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations. We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponent η.

Original language	English
Article number	120511
Journal	Science China: Physics, Mechanics and Astronomy
Volume	61
Issue number	12
DOIs	https://doi.org/10.1007/s11433-018-9266-x
State	Published - 1 Dec 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.

Funding

This work was supported by the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZD-SSW-SYS019). In addition, YongWen Zhang received a postdoctoral fellowship funded by the Kunming

Funders	Funder number
Key Research Program of Frontier Sciences
Chinese Academy of Sciences	QYZD-SSW-SYS019

Keywords

correlation function
critical phenomena
finite-size scaling
lattice model

Access to Document

10.1007/s11433-018-9266-x

Cite this

@article{b473efd23a4344a9a7a67a967a2619d4,

title = "Finite-size scaling of correlation functions in finite systems",

abstract = "We propose the finite-size scaling of correlation functions in finite systems near their critical points. At a distance r in a d-dimensional finite system of size L, the correlation function can be written as the product of |r|−(d−2+η) and a finite-size scaling function of the variables r/L and tL1/v, where t = (T − Tc)=Tc, η is the critical exponent of correlation function, and v is the critical exponent of correlation length. The correlation function only has a sigificant directional dependence when |r| is compariable to L. We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations. We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponent η.",

keywords = "correlation function, critical phenomena, finite-size scaling, lattice model",

author = "Xin Zhang and Hu, {Gao Ke} and Zhang, {Yong Wen} and Li, {Xiao Teng} and Chen, {Xiao Song}",

note = "Publisher Copyright: {\textcopyright} 2018, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2018",

month = dec,

day = "1",

doi = "10.1007/s11433-018-9266-x",

language = "אנגלית",

volume = "61",

journal = "Science China: Physics, Mechanics and Astronomy",

issn = "1674-7348",

publisher = "Science in China Press",

number = "12",

}

TY - JOUR

T1 - Finite-size scaling of correlation functions in finite systems

AU - Zhang, Xin

AU - Hu, Gao Ke

AU - Zhang, Yong Wen

AU - Li, Xiao Teng

AU - Chen, Xiao Song

PY - 2018/12/1

Y1 - 2018/12/1

N2 - We propose the finite-size scaling of correlation functions in finite systems near their critical points. At a distance r in a d-dimensional finite system of size L, the correlation function can be written as the product of |r|−(d−2+η) and a finite-size scaling function of the variables r/L and tL1/v, where t = (T − Tc)=Tc, η is the critical exponent of correlation function, and v is the critical exponent of correlation length. The correlation function only has a sigificant directional dependence when |r| is compariable to L. We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations. We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponent η.

AB - We propose the finite-size scaling of correlation functions in finite systems near their critical points. At a distance r in a d-dimensional finite system of size L, the correlation function can be written as the product of |r|−(d−2+η) and a finite-size scaling function of the variables r/L and tL1/v, where t = (T − Tc)=Tc, η is the critical exponent of correlation function, and v is the critical exponent of correlation length. The correlation function only has a sigificant directional dependence when |r| is compariable to L. We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations. We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponent η.

KW - correlation function

KW - critical phenomena

KW - finite-size scaling

KW - lattice model

UR - http://www.scopus.com/inward/record.url?scp=85054634014&partnerID=8YFLogxK

U2 - 10.1007/s11433-018-9266-x

DO - 10.1007/s11433-018-9266-x

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85054634014

SN - 1674-7348

VL - 61

JO - Science China: Physics, Mechanics and Astronomy

JF - Science China: Physics, Mechanics and Astronomy

IS - 12

M1 - 120511

ER -

Finite-size scaling of correlation functions in finite systems

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this