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 distance $r$ as $1/r^s$ in $d$ dimensions, are known to fall into two qualitatively different categories. For $s<d$ ("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. For $s>d$ ("weakly" long-range interactions) screening and hyperuniformity do not occur. Using scaling arguments, variational analysis, and Monte Carlo simulations, we find another qualitative distinction. For $s\geq d/2$ the 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 for $s\geq d/2$ and $s<d/2$ give rise to qualitatively different dependencies of the entropy, heat capacity, and energy fluctuations on temperature and density. We investigate the effect of introducing an upper cutoff distance in the pair-potential. The effect of the cutoff on energy fluctuations is strong for $s<d/2$ and negligible for $s\geq d/2$.