Nonperturbative Renormalization Flow and Essential Scaling for the Kosterlitz-Thouless Transition

TL;DR

This paper investigates the Kosterlitz-Thouless transition using nonperturbative renormalization flow, revealing essential scaling and connecting vortex effects with flow equations, providing a unified view of O(N)-models.

Contribution

It introduces a nonperturbative flow approach to describe the Kosterlitz-Thouless transition and relates vortex phenomena to flow equations, unifying models across dimensions.

Findings

Flow equations capture essential scaling behavior.

Critical exponents computed in first order derivative expansion.

Duality links vortex description with flow formalism.

Abstract

The Kosterlitz-Thouless phase transition is described by the nonperturbative renormalization flow of the two dimensional $\phi^4$-model. The observation of essential scaling demonstrates that the flow equation incorporates nonperturbative effects which have previously found an alternative description in terms of vortices. The duality between the linear and nonlinear $\sigma$-model gives a unified description of the long distance behaviour for O(N)-models in arbitrary dimension $d$. We compute critical exponents in first order in the derivative expansion.