Conformal invariance, the central charge, and universal finite-size amplitudes at criticality.

We show that for conformally invariant two-dimensional systems, the amplitude of the finite-size corrections to the free energy of an infinitely long strip of width L at criticality is linearly related to the conformal anomaly number c , for various boundary conditions. The result is confirmed by renormalization-group arguments and numerical calculations. It is also related to the magnitude of the Casimir effect in an interacting one-dimensional field theory, and to the low-temperature specific heat in quantum chains. PACS numbers: 64.60.Fr, 05.70.Jk, 68.55.–a, 75.40.–s

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