Research PaperNo Access

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

Laboratory of Semiconductor Physics, Institute of Technical Physics, Faculty of Materials Science and Applied Chemistry, Riga Technical University, P. Valdena 3/7, Riga, LV-1048, Latvia

Institute of Science and Innovative Technologies, University of Liepaja, 14 Liela Street, Liepaja LV–3401, Latvia

The MS2 Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5, Canada

E-mail Address: kaupuzs@latnet.lv

Corresponding author.

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R. V. N. Melnik

The MS2 Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5, Canada

E-mail Address: rmelnik@wlu.ca

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https://doi.org/10.1142/S0129183123500791Cited by:3 (Source: Crossref)

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 $L = 3456$ $L = 3456$ . Our estimated values of the correction-to-scaling exponent $ω$ $ω$ tend to decrease below the usually accepted value about 0.83 when the smallest lattice sizes, i.e. $L < L_{min}$ $L < L_{min}$ with $L_{min} \in [6, 64]$ $L_{min} \in [6, 64]$ , are discarded from the fits. This behavior apparently confirms some of the known estimates of the Monte Carlo renormalization group (MCRG) method, i.e. $ω \approx 0.7$ $ω \approx 0.7$ and $ω = 0.75 (5)$ $ω = 0.75 (5)$ . We discuss the possibilities that $ω$ $ω$ is either really smaller than usually expected or these values of $ω$ $ω$ describe some transient behavior which, eventually, turns into the correct asymptotic behavior at $L_{min} > 64$ $L_{min} > 64$ . We propose refining MCRG simulations and analysis to resolve this issue. Our actual MC estimations of the critical exponents $η$ $η$ and $ν$ $ν$ provide stable values $η = 0.03632 (13)$ $η = 0.03632 (13)$ and $ν = 0.63017 (31)$ $ν = 0.63017 (31)$ , which well agree with those of the conformal bootstrap method, i.e. $η = 0.0362978 (20)$ $η = 0.0362978 (20)$ and $ν = 0.6299709 (40)$ $ν = 0.6299709 (40)$ .

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