Metastability in Two Dimensions and the Effective Potential

We study analytically and numerically the decay of a metastable phase in (2+1)-dimensional classical scalar field theory coupled to a heat bath, which is equivalent to two-dimensional Euclidean quantum field theory at zero temperature. By a numerical simulation we obtain the nucleation barrier as a function of the parameters of the potential, and compare it to the theoretical prediction from the bounce (critical bubble) calculation. We find the nucleation barrier to be accurately predicted by theory using the bounce configuration obtained from the tree-level (``classical'') effective action. Within the range of parameters probed, we found that using the bounce derived from the one-loop effective action requires an unnaturally large prefactor to match the lattice results. Deviations from the tree-level prediction are seen in the regime where loop corrections would be expected to become important.Comment: 13pp, LaTex with Postscript figs, CLNS 93/1202, DART-HEP-93/0

Understanding the small object argument

The small object argument is a transfinite construction which, starting from a set of maps in a category, generates a weak factorisation system on that category. As useful as it is, the small object argument has some problematic aspects: it possesses no universal property; it does not converge; and it does not seem to be related to other transfinite constructions occurring in categorical algebra. In this paper, we give an "algebraic" refinement of the small object argument, cast in terms of Grandis and Tholen's natural weak factorisation systems, which rectifies each of these three deficiencies.Comment: 42 pages; supersedes the earlier arXiv preprint math/0702290; v2: final journal version, minor corrections onl

Expanding Bubbles in a Thermal Background

Real scalar field models incorporating asymmetric double well potentials will decay to the state of lowest energy. While the eventual nature of the system can be discerned, the determination of the dynamics of the bubble wall provides many difficulties. In the present study we investigate numerically the evolution of spherically symmetric expanding bubbles coupled to a thermal bath in 3+1 dimensions. A Markovian Langevin equation is employed to describe the interaction between bubble and bath. We find the shape and velocity of the wall to be independent of temperature, yet extremely sensitive to both asymmetry and viscosity.Comment: RevTeX, 9 pages (multicols), 9 figures, submitted to Phys. Rev.

Restricted Lie Algebras via Monadic Decomposition

We give a description of the category of restricted Lie algebras over a field (Formula presented.) of prime characteristic by means of monadic decomposition of the functor that computes the (Formula presented.)-vector space of primitive elements of a (Formula presented.)-bialgebra