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 language | English |
|---|---|
| Article number | 016120 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 74 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2006 |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
Eliminated corrections to scaling around a renormalization-group fixed point : Transfer-matrix simulation of an extended d=3 Ising model. / Nishiyama, Yoshihiro.
In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 74, No. 1, 016120, 2006.Research output: Contribution to journal › Article
}
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.
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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 -