Bubble nucleation incphi4models at all temperatures

Abstract

One possible way in which phase transitions in the early universe may have occurred is via nucleation of bubbles of the new phase (true vacuum) in the old phase (false vacuum). The technique most widely used to compute the probability of bubble nucleation is based on instanton methods in the context of the semiclassical approximation. At zero temperature in 3+1 dimensions the nucleation rate is dominated by the O(4) symmetric instanton, a sphere of radius R, while a t temperatures T >> R-' the decay is dominated by a "cylindrical" (static) instanton with O (3) invariance. There has been discussion in the literature as to whether the transition between these two regimens would be first order (discontinuity in the first derivative of the nucleation rate a t the transition temperature T,), or second order (continuity of the first derivative, but discontinuity of the second derivative a t T,). In this paper we obtain the finite temperature solutions corresponding t o the quantum and the thermal regimes, and compute their action as a function of the temperature for different values of the wall thickness in a p4 potential. Our results indicate that only for the cases of very large wall thickness a second-order transition takes place, while for all the other cases a first-order transition occurs.

Bounce solutions and the transition to thermal hopping inφ4theory

“…The aim of this paper is to investigate the nature of the phase transition for ϕ 4 theory with a ϕ 3 symmetry-breaking term and compare our results with those of Ferrera [8] who discussed a ϕ symmetry-breaking term.…”

“…Our aim is to obtain the bounce solutions at all temperatures, to compute the action and to determine the nature of the phase transition from quantum tunneling to thermal hopping. Our work therefore follows a parallel track to that of Ferrera [8], and it is of interest to compare the results for the two theories. We find that, for small values of f , the action shows a kink when plotted against temperature or its inverse β.…”

“…For this, we chose a trial value ϕ c and kept it fixed through the relaxation process (since otherwise the process is bound to diverge [8]). In the zero-and high-temperature limits, ϕT c was fixed very accurately by solving the one-dimensional equation of motion using a predictor-corrector method and shooting in ϕ c [9].…”

“…Ferrera [8] carried the investigation beyond the domain of validity of the TWA. In fact, this was the first fully field-theoretic investigation of bubble formation at arbitrary temperatures.…”

Bifurcation of a periodic instanton in a decay-rate transition

“…Recently, much attention is paid to quantum-classical decay-rate transition in various branches of physics such as spin tunneling systems [1][2][3], field theoretical models [4][5][6], and cosmology [7][8][9]. An important issue in this field is to determine the type of the decayrate transition.…”