Non-trivial exponents in the zero temperature dynamics of the 1D Ising and Potts models

1994/06/07 by Bernard Derrida, B Derrida, A. J. Bray +3 · 3 citations
Mathematics · Physics and Astronomy · #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · doi:10.1088/0305-4470/27/11/002

openalex publication_date 1994/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We consider the Glauber dynamics of the q-state Potts model in one dimension at zero temperature. Starting with a random initial configuration, we measure the density r t of spins which have never dipped from the beginning of the simulation until time t. We find that for large t, the density r t has a power-law decay (r t approximately t - theta ) where the exponent theta varies with q. Our simulations lead to theta approximately=0.37 for q=2, theta approximately=0.53 for q=3 and theta to 1 as q to infinity .

Cited by

• Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlevé VI distribution
• Distribution of domain sizes in the zero temperature Glauber dynamics of the one-dimensional Potts model
• Approach to zigzag and checkerboard patterns in spatially extended systems

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