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

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

2005-09-24

arxiv.org/abs/hep-th/0509186v2

AnnalsPhys.321:2647-2659,2006

Physics

High Energy Physics

High Energy Physics - Theory

15 pages

Scientific paper

10.1016/j.aop.2006.01.005

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).

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