Zero-temperature coarsening in the two-dimensional long-range Ising model

2020/11/30 by Henrik Christiansen, Suman Majumder, Wolfhard Janke · 1 citation
Mathematics · Physics and Astronomy · #Annihilation #Approx #Combinatorics #Condensed matter physics #Critical exponent #Dimension (graph theory) #Exponent #Fractal #Fractal dimension #Ising model #Mathematical analysis #Mathematical physics #Mathematics #Non-equilibrium thermodynamics #Opinion Dynamics and Social Influence #Phase transition #Physics #Quantum mechanics #Sigma #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Zero (linguistics) #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.103.052122

published as Phys. Rev. E 103, 052122 (2021)

arxiv created 2021/03/31 · openalex publication_date 2021/05/17 · arxiv updated 2021/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We investigate the nonequilibrium dynamics following a quench to zero temperature of the nonconserved Ising model with power-law decaying long-range interactions \ensuremath∝1/r^d+\ensuremathσ in d=2 spatial dimensions. The zero-temperature coarsening is always of special interest among nonequilibrium processes, because often peculiar behavior is observed. We provide estimates of the nonequilibrium exponents, viz., the growth exponent \ensuremathα, the persistence exponent \ensuremathθ, and the fractal dimension d_f. It is found that the growth exponent \ensuremathα\ensuremath≈3/4 is independent of \ensuremathσ and different from \ensuremathα=1/2, as expected for nearest-neighbor models. In the large \ensuremathσ regime of the tunable interactions only the fractal dimension d_f of the nearest-neighbor Ising model is recovered, while the other exponents differ significantly. For the persistence exponents \ensuremathθ this is a direct consequence of the different growth exponents \ensuremathα as can be understood from the relation d\ensuremath-d_f=\ensuremathθ/\ensuremathα; they just differ by the ratio of the growth exponents \ensuremath≈3/2. This relation has been proposed for annihilation processes and later numerically tested for the d=2 nearest-neighbor Ising model. We confirm this relation for all \ensuremathσ studied, reinforcing its general validity.

Citations

• Persistence in Nonequilibrium Systems
• Non-trivial exponents in the zero temperature dynamics of the 1D Ising and Potts models
• Persistence in systems with algebraic interaction
• Die Berechnung optischer und elektrostatischer Gitterpotentiale
• Influence of long-range interactions on the critical behavior of the Ising model
• Measurement of Persistence in 1D Diffusion
• Growth laws for phase ordering
• Persistence and first-passage properties in nonequilibrium systems
• Experimental Persistence Probability for Fluctuating Steps
• Critical behavior of the Ising model with long range interactions
• Theory of phase-ordering kinetics

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