sign of low-field currents cannot be predicted ex- actly as it depends on the number of electrons as well as disordered configurations. Our exact analy- sis can provide some physical insight to study mag- netic response in mesoscopic loop geometries. lines in Figs. 3(a) and (b). All these features are equally valid irrespective of disorder strength and disordered configurations. Thus, in brief we can say that for one-channel rings described with fixed number of electrons, sign of low-field currents can be precisely determined. At the end, we focus on the behavior of low-field magnetic response in moebius geometries. For these systems, sign of low-field currents strongly depends on the strength of intra-chain interaction ( v$_{⊥}$ ). For v$_{⊥}$ = 0, a moebius strip becomes a single channel ring, and therefore, sign of low-field currents can be mentioned exactly according to the above prescrip- tion. On the other hand for the case where v$_{⊥}$ is finite, sign of low-field currents cannot be predicted accurately as it strongly depends on the number of electrons and specific realization of disordered con- figuration in the strips. References 5 Concluding remarks To summarize, we have studied the behavior of persistent current and low-field magnetic suscepti- bility in strictly one-channel mesoscopic rings and moebius strips penetrated by magnetic flux φ . A tight-binding framework is given to describe the system, where all calculations are done numerically to study the magnetic response. In perfect rings current shows saw-tooth like variation as a func- tion of φ , while it varies continuously in disordered rings. Both for perfect and disordered rings cur- rent varies periodically with φ exhibiting φ 0 flux- quantum periodicity. In moebius strips a uncon- ventional φ 0 / 2 periodic nature of persistent current is observed for the particular case when v$_{bot}$ = 0. While, current gets back its φ 0 periodicity when electrons are able to hop along the transverse direc- tion i.e., v$_{⊥}$ = 0. In the study of low-field magnetic response we have seen that for one-channel meso- scopic rings described with constant number of elec- trons, sign of low-field currents can be mentioned precisely. While, for moebius strips with v$_{⊥}$ = 0, 8 [1] N. Byers and C. N. Yang, Phys. Rev. Lett. 7 , 46 (1961). [2] M. B¨ uttiker, Y. Imry, and R. Landauer, Phys. Lett. 96A , 365 (1983). [3] H. F. Cheung, Y. Gefen, E. K. Riedel, and W. H. Shih, Phys. Rev. B 37 , 6050 (1988). [4] H. F. Cheung and E. K. Riedel, Phys. Rev. Lett. 62 , 587 (1989). [5] G. Montambaux, H. Bouchiat, D. Sigeti, and R. Friesner, Phys. Rev. B 42 , 7647 (1990). [6] B. L. Altshuler, Y. Gefen, and Y. Imry, Phys. Rev. Lett. 66 , 88 (1991). [7] F. von Oppen and E. K. Riedel, Phys. Rev. Lett. 66 , 84 (1991). [8] A. Schmid, Phys. Rev. Lett. 66 , 80 (1991). [9] V. Ambegaokar and U. Eckern, Phys. Rev. Lett. 65 , 381 (1990). [10] G. Bouzerar, D. Poilblanc, and G. Montam- baux, Phys. Rev. B 49 , 8258 (1994). [11] T. Giamarchi and B. S. Shastry, Phys. Rev. B 51 , 10915 (1995). [12] N. Yu and M. Fowler, Phys. Rev. B 45 , 11795 (1992). [13] I. O. Kulik, Physica B 284 , 1880 (2000). [14] K. Yakubo, Y. Avishai, and D. Cohen, Phys. Rev. B 67 , 125319 (2003).