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Universal threshold for the dynamical behavior of lattice systems with long-range interactions
Romain Bachelard1, Michael Kastner
1Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil. bachelard.romain@gmail.com
Physical Review Letters
|May 18, 2013
Summary
Researchers investigated how lattice systems with long-range interactions reach equilibrium. A key threshold at α=d/2 was found, changing relaxation behavior and scaling exponents across diverse systems.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Complex Systems
Background:
- Lattice systems with long-range interactions exhibit complex dynamical properties.
- Understanding relaxation to equilibrium is crucial for characterizing system behavior.
- The influence of interaction range on dynamics is a fundamental question.
Purpose of the Study:
- To investigate the dynamical properties of lattice systems with long-range pair interactions.
- To identify the time scales governing the relaxation to equilibrium.
- To explore the role of interaction range (α) and spatial dimension (d) on these dynamics.
Main Methods:
- Analytical investigations of lattice system dynamics.
- Numerical simulations across various system types.
- Analysis of interaction potentials decaying as 1/r(α).
Main Results:
- A critical threshold at α=d/2 was identified, dependent on spatial dimension d.
- Qualitative changes in relaxation behavior occur at this threshold.
- Scaling exponents for relaxation switch to a different regime beyond the threshold.
Conclusions:
- The identified threshold at α=d/2 appears to be a universal feature.
- This universality holds across diverse systems including quantum, classical, ferromagnetic, and antiferromagnetic lattices.
- The findings provide insights into the fundamental behavior of systems with long-range interactions.
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