Winding Number Transition at Finite Temperature : Mottola-Wipf model with and without Skyrme term

TL;DR

This paper investigates the nature of winding number transitions at finite temperature in the Mottola-Wipf model, analyzing the effects of the Skyrme term and parameter values on the order of the transition.

Contribution

It provides a detailed analysis of the transition order dependence on parameters and the presence of the Skyrme term in the Mottola-Wipf model, including a new sufficient condition for first-order transitions.

Findings

First-order transition occurs for specific parameter ranges with Skyrme term.

Without Skyrme term, the transition is always first order.

Intermediate parameter values suggest a possible second-order transition.

Abstract

The winding number transition in the Mottola-Wipf model with and without Skyrme term is examined. For the model with Skyrme term the number of discrete modes of the fluctuation operator around sphaleron is shown to be dependent on the value of $\lambda m^2$. Following Gorokhov and Blatter we derive a sufficient condition for the sharp first-order transition, which indicates that first-order transition occurs when $0< \lambda m^2 < 0.0399$ and $2.148 < \lambda m^2$. In the intermediate region of $\lambda m^2$ the winding number transition is conjectured to be smooth second order. For the model without Skyrme term the winding number transition is always first order regardless of the value of parameter.