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 non-trivial 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 nu=0.6245(28) and y_h=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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Cited by in corpus (5)

• Bound-state energy of the d=3 Ising model in the broken-symmetry phase: Suppressed finite-size corrections
• Numerical diagonalization analysis of the criticality of the (2+1)-dimensional XY model: Off-diagonal Novotny's method
• Finite-size scaling of the d=5 Ising model embedded in the cylindrical geometry: An influence of the hyperscaling violation
• Criticality of the (2+1)-dimensional S=1 transverse-field Ising model with extended interactions: Suppression of corrections to scaling
• d=2 transverse-field Ising model under the screw-boundary condition: An optimization of the screw pitch