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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
Published on: May 15, 2017
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Finite-size localization scenarios in condensation transitions.
Gabriele Gotti1,2, Stefano Iubini2,3, Paolo Politi2,3
1Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy.
Physical Review. E
|June 17, 2021
Summary
This study investigates the condensation of conserved quantities in physical systems, revealing diverse localization behaviors near critical points. Numerical simulations show how system size and control parameters influence these localization scenarios.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Nonlinear Dynamics
Background:
- Condensation of conserved quantities occurs when density exceeds a critical threshold.
- Understanding localization phenomena is crucial for describing system behavior near phase transitions.
Purpose of the Study:
- To numerically investigate the condensation of a globally conserved quantity (H) on N sites.
- To analyze the dependence of the participation ratio (Y2) on system size (N) and control parameter (δ = h - hc).
- To explore localization scenarios in different physical models.
Main Methods:
- Numerical simulations of two models: a discrete nonlinear Schrödinger equation variant and a continuous zero-range process.
- Analysis of the participation ratio (Y2) as a function of system size (N) and deviation from critical density (δ).
- Characterization of localization based on the presence/absence of Y2 minimum and the exponent γ.
Main Results:
- Observed various localization scenarios for finite N near the transition point.
- Identified a critical exponent γ ≥ 2 governing the transition from delocalized to localized regimes (N* ≃ δ⁻γ).
- Found that Y2 either vanishes with increasing N (delocalized) or remains approximately constant (localized).
Conclusions:
- The study demonstrates diverse localization behaviors in systems undergoing condensation.
- The findings provide insights into the interplay between system size, control parameters, and localization phenomena.
- Comparison with single-site marginal distributions offers further understanding of condensate structure.
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