Corrections to scaling in the 3D Ising model: A comparison between MC and MCRG results

Abstract

Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation results for very large lattices with linear lattice sizes up to [Formula: see text]. Our estimated values of the correction-to-scaling exponent [Formula: see text] tend to decrease below the usually accepted value about 0.83 when the smallest lattice sizes, i.e. [Formula: see text] with [Formula: see text], are discarded from the fits. This behavior apparently confirms some of the known estimates of the Monte Carlo renormalization group (MCRG) method, i.e. [Formula: see text] and [Formula: see text]. We discuss the possibilities that [Formula: see text] is either really smaller than usually expected or these values of [Formula: see text] describe some transient behavior which, eventually, turns into the correct asymptotic behavior at [Formula: see text]. We propose refining MCRG simulations and analysis to resolve this issue. Our actual MC estimations of the critical exponents [Formula: see text] and [Formula: see text] provide stable values [Formula: see text] and [Formula: see text], which well agree with those of the conformal bootstrap method, i.e. [Formula: see text] and [Formula: see text].