Fluids with power-law repulsion: Hyperuniformity and energy fluctuations

We revisit the equilibrium statistical mechanics of a classical fluid of point-like particles with repulsive power-law pair interactions, focusing on density and energy fluctuations at finite temperature. Such long-range interactions, decaying with inter-particle distanceras1/rsinddimensions, are known to fall into two qualitatively different categories. Fors < d('strongly' long-range interactions) there are screening of correlations and suppression of large-wavelength density fluctuations (hyperuniformity). These effects eliminate density modes with arbitrarily large energy. Fors > d('weakly' long-range interactions) screening and hyperuniformity do not occur. Using scaling arguments, variational analysis, and Monte Carlo simulations, we find another qualitative distinction. Fors⩾d/2the strong repulsion at short distances leads to enhanced small-wavelength density fluctuations, decorrelating particle positions. This prevents indefinitely negative entropy and large energy fluctuations. The distinct behaviors fors⩾d/2ands