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Off-equilibrium scaling behaviors driven by time-dependent external fields in three-dimensional O(N) vector models.

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This study explores the off-equilibrium dynamics of the 3D O(N) vector model under a time-dependent magnetic field. Researchers found magnetization exhibits scaling behavior near the transition, influenced by time, scale, and system size.

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Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Dynamical Systems

Background:

  • Investigates the dynamical off-equilibrium behavior of the three-dimensional O(N) vector model.
  • Focuses on systems subjected to a slowly varying, time-dependent, spatially uniform magnetic field.
  • Examines behavior at fixed temperatures T ≤ T(c), where T(c) is the critical temperature for continuous order-disorder transitions.

Purpose of the Study:

  • To analyze the off-equilibrium scaling behavior of magnetization near the H(t)=0 transition line.
  • To understand the interplay of time, time scale, and finite size in driving this scaling.
  • To investigate hysteresis phenomena and define a scaling function for hysteresis loop area.

Main Methods:

  • Theoretical analysis of the O(N) vector model dynamics under a time-dependent magnetic field H(t).
  • Derivation of scaling behavior parametrized by specific scaling variables.
  • Numerical simulations for the Heisenberg (N=3) model using purely relaxational dynamics.

Main Results:

  • Magnetization displays off-equilibrium scaling behavior near the H(t)=0 line, dependent on time, time scale, and finite size.
  • Scaling exponents differ at the critical point and below T(c), with the latter also depending on lattice shape and boundary conditions.
  • Numerical results for the Heisenberg model confirm the predicted scaling behaviors at and below T(c).

Conclusions:

  • The study confirms predicted off-equilibrium scaling behaviors in the 3D O(N) vector model.
  • Hysteresis phenomena are discussed, and a scaling function for loop area is proposed to quantify deviation from equilibrium.
  • Findings provide insights into the non-equilibrium dynamics of magnetic systems near phase transitions.