Eliminated corrections to scaling around a renormalization-group fixed point: Transfer-matrix simulation of an extended d=3 Ising model

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Extending the parameter space of the three-dimensional (d=3) Ising model, we search for a regime of eliminated corrections to finite-size scaling. For that purpose, we consider a real-space renormalization group (RSRG) with respect to a couple of clusters simulated with the transfer-matrix (TM) method. Imposing a criterion of "scale invariance," we determine a location of the nontrivial RSRG fixed point. Subsequent large-scale TM simulation around the fixed point reveals eliminated corrections to finite-size scaling. As anticipated, such an elimination of corrections admits systematic finite-size-scaling analysis. We obtained the estimates for the critical indices as ν=0.6245 (28) and yh =2.4709 (73). As demonstrated, with the aid of the preliminary RSRG survey, the transfer-matrix simulation provides rather reliable information on criticality even for d=3, where the tractable system size is restricted severely.

Original languageEnglish
Article number016120
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume74
Issue number1
DOIs
Publication statusPublished - 2006

Fingerprint

Corrections to Scaling
Finite-size Scaling
Transfer Matrix
Renormalization Group
Ising model
Ising Model
Fixed point
scaling
Simulation
Scale Invariance
Transfer Matrix Method
simulation
Criticality
Parameter Space
Elimination
matrix methods
invariance
elimination
Three-dimensional
Estimate

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

@article{a9022681ea724abb9f7b9208cd134db4,
title = "Eliminated corrections to scaling around a renormalization-group fixed point: Transfer-matrix simulation of an extended d=3 Ising model",
abstract = "Extending the parameter space of the three-dimensional (d=3) Ising model, we search for a regime of eliminated corrections to finite-size scaling. For that purpose, we consider a real-space renormalization group (RSRG) with respect to a couple of clusters simulated with the transfer-matrix (TM) method. Imposing a criterion of {"}scale invariance,{"} we determine a location of the nontrivial RSRG fixed point. Subsequent large-scale TM simulation around the fixed point reveals eliminated corrections to finite-size scaling. As anticipated, such an elimination of corrections admits systematic finite-size-scaling analysis. We obtained the estimates for the critical indices as ν=0.6245 (28) and yh =2.4709 (73). As demonstrated, with the aid of the preliminary RSRG survey, the transfer-matrix simulation provides rather reliable information on criticality even for d=3, where the tractable system size is restricted severely.",
author = "Yoshihiro Nishiyama",
year = "2006",
doi = "10.1103/PhysRevE.74.016120",
language = "English",
volume = "74",
journal = "Physical Review E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "1",

}

TY - JOUR

T1 - Eliminated corrections to scaling around a renormalization-group fixed point

T2 - Transfer-matrix simulation of an extended d=3 Ising model

AU - Nishiyama, Yoshihiro

PY - 2006

Y1 - 2006

N2 - Extending the parameter space of the three-dimensional (d=3) Ising model, we search for a regime of eliminated corrections to finite-size scaling. For that purpose, we consider a real-space renormalization group (RSRG) with respect to a couple of clusters simulated with the transfer-matrix (TM) method. Imposing a criterion of "scale invariance," we determine a location of the nontrivial RSRG fixed point. Subsequent large-scale TM simulation around the fixed point reveals eliminated corrections to finite-size scaling. As anticipated, such an elimination of corrections admits systematic finite-size-scaling analysis. We obtained the estimates for the critical indices as ν=0.6245 (28) and yh =2.4709 (73). As demonstrated, with the aid of the preliminary RSRG survey, the transfer-matrix simulation provides rather reliable information on criticality even for d=3, where the tractable system size is restricted severely.

AB - Extending the parameter space of the three-dimensional (d=3) Ising model, we search for a regime of eliminated corrections to finite-size scaling. For that purpose, we consider a real-space renormalization group (RSRG) with respect to a couple of clusters simulated with the transfer-matrix (TM) method. Imposing a criterion of "scale invariance," we determine a location of the nontrivial RSRG fixed point. Subsequent large-scale TM simulation around the fixed point reveals eliminated corrections to finite-size scaling. As anticipated, such an elimination of corrections admits systematic finite-size-scaling analysis. We obtained the estimates for the critical indices as ν=0.6245 (28) and yh =2.4709 (73). As demonstrated, with the aid of the preliminary RSRG survey, the transfer-matrix simulation provides rather reliable information on criticality even for d=3, where the tractable system size is restricted severely.

UR - http://www.scopus.com/inward/record.url?scp=33746614446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746614446&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.74.016120

DO - 10.1103/PhysRevE.74.016120

M3 - Article

AN - SCOPUS:33746614446

VL - 74

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 1

M1 - 016120

ER -