Fluctuation-dominated phase ordering in the one-dimensional truncated inverse-distance square Ising model.

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics

Background:

• Many physical systems exhibit fluctuation-dominated phase ordering (FDPO), often in non-equilibrium states.
• An equilibrium one-dimensional truncated inverse distance square Ising (TIDSI) model was recently shown to exhibit FDPO analytically.

Purpose of the Study:

• To investigate the equilibrium one-dimensional truncated inverse distance square Ising (TIDSI) model and its fluctuation-dominated phase ordering (FDPO) properties.
• To compare analytical predictions with Monte Carlo simulations for the TIDSI model.

Main Methods:

• Analytical investigation using a cluster representation (TIDSI-CL).
• Monte Carlo simulations of the TIDSI model.
• Analysis of correlation functions, domain size distribution, and aging behavior.

Main Results:

• The TIDSI-CL model allows an unbounded range for the interaction ratio c, unlike the narrow range in the original TIDSI model.
• Simulations validated analytical results within the allowed range of c.
• A broad near-critical region was observed due to strong correlation length growth.
• Effective cusp exponent α^{eff} was identified.
• Coarsening dynamics showed consistency with equilibrium properties when system size was replaced by coarsening length.
• Aging autocorrelation function exhibited two distinct scaling forms.

Conclusions:

• The equilibrium TIDSI model successfully demonstrates FDPO, consistent with analytical predictions.
• The model exhibits unique critical and dynamic behaviors, including a broad critical region and distinct aging scaling.
• The study provides insights into equilibrium systems exhibiting FDPO and their complex dynamics.