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Test of modular invariance for finite XXZ chains

The central charge c of the Virasoro algebra is determined using its relation to the set of anomalous dimensions of the scaling fields for the critical anisotropic Heisenberg chain. The results obtained by exactly solving the Bethe ansatz for N<or=4 are compared with the standard procedure for calculating c in the whole region of anisotropy. For odd N the system is no longer modular invariant and the analogous averaging leads to an anisotropy-dependent function which has been calculated.