  Twenty three years ago, cosmological N-body simulations revealed
quasi-universal NFW dark matter halos, whose physical origin is still unclear.
This work tries to solve this issue by Landau-Ginzburg (LG) theory in
equilibrium statistical mechanics. We replace the order parameter in LG theory
by density and consider the dark matter halos as fluctuations from the
equilibrium state of the background, which can be the main halos for the
subhalos, or the homogeneous and isotropic Universe for the galaxy cluster
halos. With the assumption that the fluctuations of Helmholtz free energy
depend mainly on the density and its gradient, which is shown to be consistent
with the behavior of the power spectrum near the cluster scale, we can easily
obtain the universal $r^{-1}$ cusp of the equilibrium dark matte halo without
other requirements. This work strongly suggests that more studies should be
done for the self-gravitating systems by statistical mechanics.

Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies;Statistical Mechanics