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In this paper, we propose a quantum field theoretical renormalization groupapproach to the vortex dynamics of magnetically coupled layeredsuperconductors, to supplement our earlier investigations on theJosephson-coupled case. We construct a two-dimensional multi-layer sine-Gordontype model which we map onto a gas of topological excitations. With a specialchoice of the mass matrix for our field theoretical model, vortex dominatedproperties of magnetically coupled layered superconductors can be described.The well known interaction potentials of fractional flux vortices areconsistently obtained from our field-theoretical analysis, and the physicalparameters (vortex fugacity and temperature parameter) are also identified. Weanalyse the phase structure of the multi-layer sine--Gordon model by adifferential renormalization group method for the magnetically coupled casefrom first principles. The dependence of the transition temperature on thenumber of layers is found to be in agreement with known results based on othermethods.

Applicability of layered sine-Gordon models to layered superconductors: II. The case of magnetic coupling