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Evidence for hidden order in a nonlinear model elastic system.
1Department of Materials Science and Engineering, 1235 E. James E Rogers Way, University of Arizona, Tucson, AZ 85721, United States of America.
Summary
Hidden order, previously seen in quantum systems, emerges in a classical mechanical model. This phenomenon, characterized by a string order parameter, reveals long-range correlations in locally disordered systems.
Area of Science:
- Physics
- Condensed Matter Physics
- Non-linear Dynamics
Background:
- Hidden order is a complex phenomenon observed in strongly correlated systems, often linked to topological order in quantum mechanics.
- Local order parameters may not fully capture the emergent properties of certain physical systems.
Purpose of the Study:
- To demonstrate the emergence of hidden order in a classical, 1D non-linear mechanical system.
- To investigate the role of a biquadratic term in inducing hidden order and distinct phases.
Main Methods:
- Development of a 1D non-linear classical mechanical model with rotational degrees of freedom.
- Introduction of a biquadratic term in the potential energy to create a bistable system.
- Analysis of system phases using Néel and string order parameters.
Main Results:
- Four distinct phases were identified by varying the biquadratic term strength, with three being locally disordered.
- A string order parameter revealed correlations with significantly longer range than the Néel order parameter.
- The hidden order correlation length diverged with a critical exponent of ~0.5 as kinetic energy decreased.
Conclusions:
- Hidden order can emerge in classical mechanical systems, not just quantum ones.
- Instability and non-linearity are critical factors in generating non-local, long-range correlations in apparently disordered systems.
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