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

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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 - Aug 4 2006

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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