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Low-temperature Glauber dynamics under weak competing interactions.

M D Grynberg1

  • 1Departamento de Física, Universidad Nacional de La Plata, 1900 La Plata, Argentina.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 15, 2015
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Summary
This summary is machine-generated.

Investigating Glauber dynamics in Ising spin chains reveals distinct low-temperature behaviors. Weakly frustrated systems exhibit near-ballistic coarsening, while noncompeting interactions show diffusive dynamics.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Spin Dynamics

Background:

  • Glauber dynamics models the stochastic behavior of magnetic systems.
  • Ising spin chains with competing interactions exhibit complex low-temperature properties.
  • Understanding coarsening dynamics is crucial for characterizing phase transitions.

Purpose of the Study:

  • To investigate the low-temperature, nonzero-temperature regimes of Glauber dynamics in Ising spin chains.
  • To analyze the impact of first- and second-neighbor interactions (J1, J2) on spin chain kinetics.
  • To characterize the asymptotic behavior of frustrated and noncompeting spin systems.

Main Methods:

  • Finite-size scaling analysis of relaxation times.
  • Computational modeling of Glauber dynamics.
  • Theoretical analysis of kinetic exponents and coarsening velocities.

Main Results:

  • For weakly frustrated systems (0 < -J2/|J1| < 1), dynamics are ergodic and coarsening at T→0+ with a near-ballistic exponent z ≈ 1.03(2) and slow growth velocities.
  • Noncompeting interactions lead to diffusive coarsening length scales.
  • The study distinguishes between metastable, noncoarsening dynamics at T=0 and ergodic, coarsening dynamics at T→0+.

Conclusions:

  • The asymptotic kinetics of Ising spin chains depend significantly on the nature and strength of competing interactions.
  • Weak frustration induces anomalous, near-ballistic coarsening at vanishing temperatures.
  • Diffusive coarsening is characteristic of noncompeting interaction regimes.