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

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. Nándori, S. Nagy, K. Sailer and U. D. Jentschura, Nucl. Phys. B 725, 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 β2 c,N = 8Nπ, where N is the number of layers (or flavours in terms of the multi-flavour Schwinger model).