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Critical dynamical exponent of the two-dimensional scalar ϕ4 model with local moves
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Zhong, Wei, Barkema, Gerard T., Panja, Debabrata and Ball, Robin (2018) Critical dynamical exponent of the two-dimensional scalar ϕ4 model with local moves. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 98 (6). 062128 . doi:10.1103/PhysRevE.98.062128 ISSN 1550-2376.
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Official URL: https://doi.org/10.1103/PhysRevE.98.062128
Abstract
We study the scalar one-component two-dimensional (2D) ϕ^4 model by computer simulations, with local Metropolis moves. The equilibrium exponents of this model are well established, e.g., for the 2D ϕ^4 model γ=1.75 and ν=1. The model has also been conjectured to belong to the Ising universality class. However, the value of the critical dynamical exponent z_c is not settled. In this paper, we obtain z_c for the 2D ϕ^4 model using two independent methods: (a) by calculating the relative terminal exponential decay time τ for the correlation function ⟨Φ(t)Φ(0)⟩, and thereafter fitting the data as τ∼L^zc, where L is the system size, and (b) by measuring the anomalous diffusion exponent for the order parameter, viz., the mean-square displacement ⟨ΔΦ^2(t)⟩∼t^c as c=γ/(νz_c), and from the numerically obtained value c≈0.80, we calculate z_c. For different values of the coupling constant λ, we report that z_c=2.17±0.03 and z_c=2.19±0.03 for the two methods, respectively. Our results indicate that z_c is independent of λ, and is likely identical to that for the 2D Ising model. Additionally, we demonstrate that the generalized Langevin equation formulation with a memory kernel, identical to those applicable for the Ising model and polymeric systems, consistently captures the observed anomalous diffusion behavior.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QC Physics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||||
Library of Congress Subject Headings (LCSH): | Phase transformations (Statistical physics), Ising model, Monte Carlo method, Langevin equations | ||||||
Journal or Publication Title: | Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) | ||||||
Publisher: | American Physical Society | ||||||
ISSN: | 1550-2376 | ||||||
Official Date: | 19 December 2018 | ||||||
Dates: |
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Volume: | 98 | ||||||
Number: | 6 | ||||||
Article Number: | 062128 | ||||||
DOI: | 10.1103/PhysRevE.98.062128 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Reuse Statement (publisher, data, author rights): | © 2018 American Physical Society | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 21 December 2018 | ||||||
Date of first compliant Open Access: | 21 December 2018 | ||||||
RIOXX Funder/Project Grant: |
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