Self-interacting scalar fields at high-temperature
  We study two self-interacting scalar field theories in their high-temperature
limit using path integrals on a lattice. We first discuss the formalism and
recover known potentials to validate the method. We then discuss how these
theories can model, in the high-temperature limit, the strong interaction and
General Relativity. For the strong interaction, the model recovers the known
phenomenology of the nearly static regime of heavy quarkonia. The model also
exposes a possible origin for the emergence of the confinement scale from the
approximately conformal Lagrangian. Aside from such possible insights, the main
purpose of addressing the strong interaction here --given that more
sophisticated approaches already exist-- is mostly to further verify the
pertinence of the model in the more complex case of General Relativity for
which non-perturbative methods are not as developed. The results have important
implications on the nature of Dark Matter. In particular, non-perturbative
effects naturally provide flat rotation curves for disk galaxies, without need
for non-baryonic matter, and explain as well other observations involving Dark
Matter such as cluster dynamics or the dark mass of elliptical galaxies.
