Effective Action and Phase Structure of Multi-Layer Sine-Gordon Type Models

TL;DR

This paper investigates the phase structure of multi-layer sine-Gordon models, revealing how the number of layers influences the critical coupling for phase transitions, with implications for vortex behavior in high-temperature superconductors.

Contribution

It extends the analysis of two-layer sine-Gordon models to N layers, identifying the key role of mass eigenvalues and deriving the critical coupling for phase transitions in multi-layer systems.

Findings

Critical coupling for phase transition: N layers is 8 N  .

Identification of periodic modes in multi-layer structure.

Extension of vortex behavior analysis to realistic multi-layer superconductors.

Abstract

We analyze the effective action and the phase structure of N-layer sine-Gordon type models, generalizing the results obtained for the two-layer sine-Gordon model found in [I. Nandori, S. Nagy, K. Sailer and U. D. Jentschura, Nucl. Phys. B725, 467-492 (2005)]. Besides the obvious field theoretical interest, the layered sine-Gordon model has been used to describe the vortex properties of high transition temperature superconductors, and the extension of the previous analysis to a general N-layer model is necessary for a description of the critical behaviour of vortices in realistic multi-layer systems. The distinction of the Lagrangians in terms of mass eigenvalues is found to be the decisive parameter with respect to the phase structure of the N-layer models, with neighbouring layers being coupled by quadratic terms in the field variables. By a suitable rotation of the field variables, we identify the periodic modes (without explicit mass terms) in the N-layer structure, calculate the effective action and determine their Kosterlitz-Thouless type phase transitions to occur at a coupling parameter \beta^2_{c} = 8 N \pi, where N is the number of layers (or flavours in terms of the multi-flavour Schwinger model).