Multiscale complexity of correlated Gaussians

Area of Science:

• Statistical Mechanics
• Complex Systems Analysis

Background:

• Understanding complex systems requires robust analytical tools.
• Multiscale complexity offers a novel approach to characterizing system dynamics.

Purpose of the Study:

• To apply a new multiscale complexity measure to Gaussian models.
• To investigate universal behaviors in systems with varying interaction structures.
• To interpret the underlying structure of systems using pair correlation data.

Main Methods:

• Application of a recently developed multiscale complexity measure.
• Analysis of Gaussian models with continuous spins and bilinear interactions.
• Examination of diverse interaction matrix structures.

Main Results:

• Identified two universal behaviors of the complexity profile.
• Observed exponential decay in non-frustrated systems, indicating small-scale fluctuations.
• Found logarithmically diverging profiles near critical points for non-frustrated systems, describing collective modes.
• Detected oscillations in complexity for frustrated variables, signifying global or local constraints.

Conclusions:

• Multiscale complexity is a valuable tool for interpreting system structures.
• The measure effectively differentiates between frustrated and non-frustrated system dynamics.
• Findings provide insights into the spectrum of collective modes and system constraints.