Central Charge and Universal Combinations of Amplitudes in Two-Dimensional Theories Away from Criticality

For a general isotropic two-dimensional theory near criticality, the universal singular free energy per correlation volume $f_s{\xi }^2$ is equal to $-\left(\frac{c}{12}\pi \right)(2-\alpha ){(1-\alpha )}^{-1\mathrm{}}$, where $c$ is the central charge of the theory at criticality, $\alpha$ is the usual specific-heat exponent, and $\xi$ is defined (for $\alpha >0\mathrm{}$) in terms of the second moment of the energy correlations. Some generalizations of this result are also noted.