Corrections to finite-size scaling in the 3D Ising model based on nonperturbative approaches and Monte Carlo simulations

J. Kaupužs, R. V. N. Melnik and J. Rimšāns
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J. Kaupužs: Institute of Technical Physics, Riga Technical University, Laboratory of Semiconductor Physics, Paula Valdena Str. 3/7, LV-1048, Riga, Latvia†Institute of Mathematical Sciences and Information 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
R. V. N. Melnik: #x2021;The MS2 Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5, Canada§BCAM - Basque Center for Applied Mathematics, E48009 Bilbao, Spain
J. Rimšāns: #x2020;Institute of Mathematical Sciences and Information 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

International Journal of Modern Physics C (IJMPC), 2017, vol. 28, issue 04, 1-20

Abstract: Corrections to scaling in the 3D Ising model are studied based on nonperturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L. Analytical arguments show the existence of corrections with the exponent (γ−1)∕ν≈0.38, the leading correction-to-scaling exponent being ω≤(γ−1)∕ν. A numerical estimation of ω from the susceptibility data within 40≤L≤2560 yields ω=0.21(29), in agreement with this statement. We reconsider the MC estimation of ω from smaller lattice sizes, L≤384, using different finite-size scaling methods, and show that these sizes are still too small, since no convergence to the same result is observed. In particular, estimates ranging from ω=0.866(21) to ω=1.247(73) are obtained, using MC data for thermodynamic average quantities, as well as for partition function zeros. However, a trend toward smaller ω values is observed in one of these cases in a refined estimation from extended data up to L=1536. We discuss the influence of ω on the estimation of critical exponents η and ν.

Keywords: Ising model; corrections to scaling; nonperturbative methods; Feynman diagrams; critical couplings; Monte Carlo simulation (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S0129183117500449

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