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Using the effective conformal field theory for the quantum Hall edge stateswe propose a compact and convenient scheme for the computation of the periods,amplitudes and temperature behavior of the chiral persistent currents and themagnetic susceptibilities in the mesoscopic disk version of the Z_k parafermionquantum Hall states in the second Landau level. Our numerical calculations showthat the persistent currents are periodic in the Aharonov-Bohm flux with periodexactly one flux quantum and have a diamagnetic nature. In the high-temperatureregime their amplitudes decay exponentially with increasing the temperature andthe corresponding exponents are universal characteristics of non-Fermi liquids.Our theoretical results for these exponents are in perfect agreement with thoseextracted from the numerical data and demonstrate that there is in general anon-trivial contribution coming from the neutral sector. We emphasize thecrucial role of the non-holomorphic factors, first proposed by Cappelli andZemba in the context of the conformal field theory partition functions for thequantum Hall states, which ensure the invariance of the annulus partitionfunction under the Laughlin spectral flow.Comment: 14 pages, RevTeX4, 7 figures (eps

Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux