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Corrections to finite-size scaling in the φ4 model on square lattices

Author

Listed:
  • J. Kaupužs

    (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

    (#x2020;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

    (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)

Abstract

Corrections to scaling in the two-dimensional (2D) scalar φ4 model are studied based on nonperturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L (4≤L≤1536) and different values of the φ4 coupling constant λ, i.e. λ=0.1, 1, 10. According to our analysis, amplitudes of the nontrivial correction terms with the correction–to–scaling exponents ωℓ<1 become small when approaching the Ising limit (λ→∞), but such corrections generally exist in the 2D φ4 model. Analytical arguments show the existence of corrections with the exponent 3∕4. The numerical analysis suggests that there exist also corrections with the exponent 1∕2 and, perhaps, also with the exponent about 1∕4, which are detectable at λ=0.1. The numerical tests provide an evidence that the structure of corrections to scaling in the 2D φ4 model differs from the usually expected one in the 2D Ising model.

Suggested Citation

  • J. Kaupužs & R. V. N. Melnik & J. Rimšāns, 2016. "Corrections to finite-size scaling in the φ4 model on square lattices," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(09), pages 1-24, September.
    • Handle: RePEc:wsi:ijmpcx:v:27:y:2016:i:09:n:s0129183116501084
    DOI: 10.1142/S0129183116501084
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