Friedel transition in a modified XY model

TL;DR

This paper investigates a modified three-dimensional XY model with anisotropic coupling, revealing a Friedel transition characterized by two phase transitions, including a Kosterlitz-Thouless transition and a transition to three-dimensional coherence.

Contribution

It demonstrates the existence of a Friedel transition in a specific class of anisotropic XY models with modified interlayer coupling.

Findings

Two phase transitions identified: Kosterlitz-Thouless and 3D coherence transition.

Friedel transition occurs only with modified interlayer coupling.

Layer decoupling does not happen with standard Josephson coupling.

Abstract

Weakly coupled superconducting layers are described by the three-dimensional XY model with strong coupling in two directions and weak coupling in the third direction. For the usual Josephson-type interplane coupling the coherence between the layers is lost at the same temperature as that within the layers. Thus a low-temperature layer decoupling due to a proliferation of fluxons between planes, as proposed by Friedel, does not occur in this case. However, for a modified interplane coupling there are two phase transitions, one of a Kosterlitz-Thouless type from a disordered high-temperature phase to an intermediate phase with phase coherence only parallel to the layers, the second from this effectively two-dimensional phase to a three-dimensional phase with coherence in all directions and a finite "n-state" order parameter. Thus we do find a "Friedel transition" for this special class of models.