Finite-size scaling in the ageing dynamics of the $1D$ Glauber-Ising model

Abstract

Single-time and two-time correlators are computed exactly in the $1D$ Glauber-Ising model after a quench to zero temperature and on a periodic chain of finite length $N$, using a simple analytical continuation technique. Besides the general confirmation of finite-size scaling in non-equilibrium dynamics, this allows to test the scaling behaviour of the plateau height $C_{\infty }^{(2)}$ to which the two-time auto-correlator converges, when deep into the finite-size regime.

arXiv commentLatex2e, 29 pp, 5 figures; in memoriam Ralph Kenna

References in corpus (23)

• Theory of Phase Ordering Kinetics
• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Response of non-equilibrium systems at criticality: Exact results for the Glauber-Ising chain
• The Energy-Scaling Approach to Phase-Ordering Growth Laws
• Aging in the long-range Ising model
• Modified fluctuation-dissipation theorem near non-equilibrium states and applications to the Glauber-Ising chain
• One dimensional phase-ordering in the Ising model with space decaying interactions
• Coarsening and Aging of Lattice Polymers: Influence of Bond Fluctuations
• On the Slowing Down of Spin Glass Correlation Length Growth:simulations meet experiments
• Universality in the time correlations of the long-range 1d Ising model
• Understanding nonequilibrium scaling laws governing collapse of a polymer
• Coexistence of coarsening and mean field relaxation in the long-range Ising chain
• Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods
• Dynamic Heterogeneity in the Glauber-Ising chain
• Dimensional crossover in the aging dynamics of spin glasses in a film geometry
• Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method
• Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method
• On integral representations and asymptotics of some hypergeometric functions in two variables
• Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington-Kirkpatrick model
• Non-universality of aging during phase separation of the two-dimensional long-range Ising model
• Non-equilibrium relaxations: ageing and finite-size effects
• Crossover properties of a one-dimensional reaction-diffusion process with a transport current
• Ordering kinetics with long-range interactions: interpolating between voter and Ising models

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• Harnessing finite-size effects to gauge aging in the $2D$ Ising model
• Exact solution of the Glauber-Ising model on the finite-length semi-open chain
• Schrödinger-invariance in the voter model