Real scalar phase transitions: a nonperturbative analysis
Abstract
We study the thermal phase transitions of a generic real scalar field, without a Z_{2}symmetry, referred to variously as an inert, sterile or singlet scalar, or ϕ^{3} + ϕ^{4} theory. Such a scalar field arises in a wide range of models, including as the inflaton, or as a portal to the dark sector. At high temperatures, we perform dimensional reduction, matching to an effective theory in three dimensions, which we then study both perturbatively to threeloop order and on the lattice. For strong firstorder transitions, with large treelevel cubic couplings, our lattice MonteCarlo simulations agree with perturbation theory within error. However, as the size of the cubic coupling decreases, relative to the quartic coupling, perturbation theory becomes less and less reliable, breaking down completely in the approach to the Z_{2}symmetric limit, in which the transition is of second order. Notwithstanding, the renormalisation group is shown to significantly extend the validity of perturbation theory. Throughout, our calculations are made as explicit as possible so that this article may serve as a guide for similar calculations in other theories.
 Publication:

Journal of High Energy Physics
 Pub Date:
 April 2021
 DOI:
 10.1007/JHEP04(2021)057
 arXiv:
 arXiv:2101.05528
 Bibcode:
 2021JHEP...04..057G
 Keywords:

 Cosmology of Theories beyond the SM;
 Effective Field Theories;
 Lattice Quantum Field Theory;
 Thermal Field Theory;
 High Energy Physics  Phenomenology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 43 pages, 14 figures