Phase ordering dynamics of the random-field long-range Ising model in one dimension

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Complex Systems

Background:

• The one-dimensional random-field Ising model (RFIM) describes systems with competing ferromagnetic interactions and quenched disorder.
• Phase ordering dynamics in RFIM are typically characterized by domain growth and coarsening.
• Nearest-neighbor interactions lead to specific scaling behaviors in domain growth.

Purpose of the Study:

• To investigate the impact of long-range (LR) interactions on the phase ordering dynamics of the 1D RFIM.
• To understand how LR interactions modify the characteristic domain growth and coarsening processes.
• To analyze the competition between LR interaction-induced driving forces and random-field pinning forces.

Main Methods:

• Theoretical analysis of the 1D RFIM with ferromagnetic coupling decaying as r^{-(1+σ)}.
• Examination of domain size evolution R(t) under varying LR interaction strengths (σ).
• Study of spatial correlation and autocorrelation functions of the magnetization field.

Main Results:

• LR interactions alter preasymptotic growth from R(t)∼t^{1/2} to R(t)∼t and then R(t)∼t^{1/(1+σ)}.
• Asymptotic logarithmic growth R(t)∼(lnt)^{α(σ)} is modified with α(σ)<2, indicating slower dynamics.
• Spatial correlation exhibits superuniversality for all σ; autocorrelation shows superuniversality for σ<1.

Conclusions:

• LR interactions accelerate short-time domain growth but decelerate asymptotic dynamics in the 1D RFIM.
• A balance between random-field pinning and LR driving forces governs the observed dynamics.
• Superuniversality in correlation functions depends on the range of LR interactions.