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

TL;DR

This paper identifies a regime in an extended 3D Ising model where corrections to finite-size scaling are eliminated, enabling more accurate determination of critical indices through transfer-matrix simulations.

Contribution

It introduces a real-space renormalization group approach combined with transfer-matrix methods to find fixed points with eliminated scaling corrections in the 3D Ising model.

Findings

Elimination of corrections to finite-size scaling near the fixed point

Precise estimates of critical exponents nu and y_h

Transfer-matrix simulations are reliable for criticality analysis in 3D

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.