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Nonequilibrium dynamics in Ising-like models with biased initial condition.

Reshmi Roy1, Parongama Sen1

  • 1Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India.

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Summary
This summary is machine-generated.

We studied dynamical fixed points in Ising-like models using Glauber dynamics. An exponent dependent on coordination number z was found, impacting phase diagrams and exit probabilities.

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Area of Science:

  • Statistical Physics
  • Complex Systems Dynamics
  • Computational Physics

Background:

  • Investigating equilibrium and non-equilibrium properties of magnetic models is crucial for understanding emergent phenomena.
  • Glauber dynamics provides a framework for simulating spin systems and analyzing their relaxation behavior.
  • The role of dimensionality and connectivity (coordination number z) significantly influences system dynamics.

Purpose of the Study:

  • To analyze the dynamical fixed points of zero-temperature Glauber dynamics in Ising-like models.
  • To determine the influence of the coordination number (z) on system stability and phase transitions.
  • To characterize the exit probability and its scaling behavior in various lattice models.

Main Methods:

  • Mean-field calculations to analyze stability of fixed points and derive an exponent dependent on coordination number z.
  • Numerical simulations of the Ising model for both mean-field and short-range interactions on lattices with varying z.
  • Analysis of exit probability E(x0) and data collapse using scaling variables for finite-size dependent behavior.

Main Results:

  • Identified a coordination number-dependent exponent in Ising model stability analysis.
  • Obtained a phase diagram for the generalized voter model and confirmed E(x0)=x0 for mean-field z=2 (conserved magnetization).
  • Observed finite-size dependent nonlinear behavior in exit probability for larger z, with successful data collapse using specific scaling functions.

Conclusions:

  • The coordination number z plays a critical role in determining the dynamical behavior and stability of Ising-like models.
  • The exit probability exhibits universal scaling behavior, characterized by a specific scaling variable and function, across different models and dimensions.
  • Further investigation into the universality of the exponent and scaling factors is warranted for a comprehensive understanding of these spin dynamics.