Influence of vortex-loop fluctuations on equilibrium properties of layered superconductors. II. Field-theoretical approach

In layered superconductors with weak interlayer coupling, fluctuations involving thermal excitation of vortex loops parallel to the layers occur over a wide range of temperatures below ${\mathit{T}}_{\mathit{c}}$. The problem of calculating the system’s equilibrium thermal and magnetic properties taking into account these fluctuations has been formulated by the author (in the preceding paper) in terms of point vortices interacting through an effective Hamiltonian ${\mathit{scrH}}_{\mathrm{eff}}$. Here a field-theoretical expression for ${\mathit{scrH}}_{\mathrm{eff}}$, involving the functional integral over a scalar field is obtained. This expression, which is of general validity, is used to derive and justify mean-field-like approximations for ${\mathit{scrH}}_{\mathrm{eff}}$.