ABSENCE OF INFLATION SYMMETRICAL COMMENSURATE STATES IN INFLATION SYMMETRICAL NETWORKS

In this paper we present measurements of the normal-to superconducting phase boundary T(c)(H) for three different networks possessing inflat ion symmetry. Fluxoid quantization constraints induce the formation of a lattice of fluxoid quanta for any non-zero perpendicular magnetic f ield, and at particular fields, T(c)(H) exhibits cusp-like structure i ndicating that the lattice is commensurate with the underlying network geometry. For inflation symmetric networks studied in the past, all c ommensurate states have always been related to the inflation symmetry. In the three networks studied here, none of the commensurate phase bo undary structure derives from the inflation symmetry. We propose that this structure can instead be understood by considering the Fourier tr ansform of the network geometry and that the transform actually provid es a more universal prescription for the identification of commensurat e states. The relevance of the transform (as opposed to the inflation symmetry) in determining commensurate states in two dimensions is cons istent with analytical work performed for one dimensional systems.