(A) study on the phase transition of decay rate in field theoreticl models

Abstract

The phase transition of decay rate from quantum tunneling to thermal activity regime is investigated in several field theoretical models. The asymmetric double well potential model in which the asymmetric term is given by fφ or $\delta\phi^3$, is treated in various dimensions such as (1+1) and (1+3)-dimension. By applying two independent criteria for the first-order transition to the models in (1+3)-dimensional case, the upper and lower bounds of critical value of the parameter of the asymmetric term are obtained as 1.02 ＜ δ ＜1.42. And we study the relationship between the number of negative modes of the periodic instanton in the vicinity of the sphaleron solution and the type of decay rate transition. We re-drive the criterion for the first order transition which was reported by Gorokhov and Blatter by counting the number of negative modes. For the first order transtion case, the lowest positive mode at low energy periodic instanton becomes additional negative mode at high energy regime, while for the second order case, there is only one negative mode in the full range of energy. And we examine the winding number transition in the Mottola-Wipf model with and without Skyrme term. For the model with Skyrme term the number of discrete modes of the fluctuation operator around the sphaleron is shown to be dependent of the parameter. Following Gorokhov and Blatter we derive the sufficient condition for the sharp first order phase transition, which indicates that first order transition occurs when $0 ＜ \lambda\omega^2 ＜ 0.0399$ and $2.148 ＜ \lambda\omega^2$. In the intermediate region of $\lambda\omega^2$ the winding number transition is conjectured to be smooth second order. While, for the model without Skyrme term the winding number transition is always first order regardless of the parameter.