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Virtual walks in the Ising model: Finite-time scaling.

Amit Pradhan1, Parongama Sen1, Sagnik Seth2

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

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Summary
This summary is machine-generated.

This study uses a virtual walk to analyze spin dynamics in the Ising model. Results reveal a distinct temperature-dependent change in spin behavior and a time-dependent critical point estimation.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics
  • Condensed Matter Physics

Background:

  • The Ising model is a fundamental model in statistical mechanics for studying magnetism and phase transitions.
  • Understanding spin dynamics under non-equilibrium conditions is crucial for various physical phenomena.

Purpose of the Study:

  • To analyze the dynamics of spins in the Ising model using a novel virtual walk scenario.
  • To investigate the system's behavior when quenched from high to low temperatures.
  • To explore non-equilibrium phenomena and estimate critical points.

Main Methods:

  • A virtual walk scenario is employed, where each spin's evolution is tied to its current state.
  • The Glauber scheme is used for quenching the system in one and two dimensions.
  • Probability distributions of walker displacement and average displacement over time are calculated.
  • Finite-time scaling analysis is applied to quantities in two dimensions.

Main Results:

  • A distinct change in the probability distribution of walker displacement is observed with increasing temperature.
  • A non-equilibrium region in average displacement persists longer than bulk magnetization.
  • A time-dependent critical point can be estimated using two distinct methods.
  • Virtual walks generated from local spin energy are introduced.
  • Finite-time scaling in 2D shows consistency with known critical exponents.

Conclusions:

  • The virtual walk method provides a valuable tool for studying non-equilibrium dynamics in the Ising model.
  • The approach allows for the detection and estimation of critical phenomena even in finite time.
  • Results validate the consistency of the virtual walk method with established critical exponent values.