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The energy and persistent current spectra for a relativistic fermion on a ring are studied in detail. The nonlinear nature of persistent current in relativistic regime and its dependence on particle mass and ring radius are analysed thoroughly. For a particular ring radius, we find the existence of a critical mass at which the single ring current does not depend on the flux. In lower mass regime, the total current spectrum shows plateaus at different height which appears periodically. Thedoi:10.1155/2013/592402 fatcat:2s7e6ipavvc4rmafe456oa7q3i