arXiv subjects
Publications and source records attributed to S. Bornholdt.
The critical behaviour of a system of two coupled scalar fields in three dimensions is studied within the formalism of the effective average action. The fixed points of the system are identified and the crossover between them is described in detail. Besides the universal critical behaviour, the flow of the coarse grained free energy also describes the approach to scaling.
Non-perturbative exact flow equations describe the scale dependence of the effective average action. We present a numerical solution for an approximate form of the flow equation for the potential in a three-dimensional N-component scalar field theory. The critical behaviour, with associated critical exponents, can be inferred with good accuracy.
Two-scalar theories at high temperature exhibit a rich spectrum of possible critical behaviour, with a second or first order phase transition. In the vicinity of the critical temperature one can observe critical exponents, tricritical points and crossover behaviour. None of these phenomena are visible to high temperature perturbation theory.
We explore the Coleman-Weinberg phase transition in regions outside the validity of perturbation theory. For this purpose we study a Euclidean field theory with two scalars and discrete symmetry in four dimensions. The phase diagram is established by a numerical solution of a suitable truncation of exact non-perturbative flow equations. We find regions in parameter space where the phase transition (in dependence on the mass term) is of the second or the first order, separated by a triple point. Our quantitative results for the first order phase transition compare well to the standard perturbative Coleman-Weinberg calculation of the effective potential.