Absence of inflation symmetric commensurate states in inflation symmetric networks

(Received 14 September 1993, accepted 9 December 1993)

Abstract
In this paper we présent measurements of thé normal-to superconducting phase boundary T_c(H) for three différent networks possessing inflation symmetry. Fluxoid quantization constraints induce thé formation of a lattice of fluxoid quanta for any non-zéro perpendicular magnetic field, and at particular fields, T_c(H) exhibits cusp-like structure indicating that thé lattice is commensurate with thé underlying network geometry. For inflation symmetric networks studied in thé part, all commensurate states have always been related to thé inflation symmetry. In thé three networks studied here, none of thé commensurate phase boundary structure derives from thé inflation symmetry. We propose that this structure can instead be understood by considering thé Fourier transform of thé network geometry and that thé transform actually provides a more universal prescription for thé identification of commensurate states. The relevance of thé transform (as opposed to thé inflation symmetry) in determining commensurate states in two dimensions is consistent with analytical work performed for one dimensional systems.