Fluids with power-law repulsion: Hyperuniformity and energy fluctuations

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Classical fluids

Background:

• Power-law interactions in classical fluids exhibit two categories: strongly long-range (sd).
• Strongly long-range interactions lead to correlation screening and hyperuniformity, suppressing large-wavelength density fluctuations.
• Weakly long-range interactions do not exhibit these screening effects.

Purpose of the Study:

• To investigate density and energy fluctuations in classical fluids with repulsive power-law pair interactions at finite temperatures.
• To identify qualitative distinctions in fluid behavior based on interaction range (s) and dimensionality (d).
• To analyze the impact of short-range repulsion and interaction cutoffs on thermodynamic properties.

Main Methods:

• Scaling arguments
• Variational analysis
• Monte Carlo simulations

Main Results:

• A new qualitative distinction is found for s ≥ d/2, where strong short-range repulsion enhances small-wavelength density fluctuations, preventing negative entropy and large energy fluctuations.
• Fluid behaviors differ qualitatively for s ≥ d/2 and s < d/2, affecting dependencies of entropy, heat capacity, and energy fluctuations on temperature and density.
• Introducing an upper cutoff in the pair-potential significantly impacts energy fluctuations for s < d/2 but has a negligible effect for s ≥ d/2.

Conclusions:

• The exponent 's' in power-law interactions critically determines fluid behavior, leading to distinct regimes of density and energy fluctuations.
• Stronger repulsions (s ≥ d/2) stabilize the system against large energy fluctuations, unlike weaker repulsions (s < d/2).
• Interaction cutoffs play a role in energy fluctuation dynamics, with their significance depending on the interaction range.