Central charge and universal combinations of amplitudes in two-dimensional theories away from criticality.

TLDR: The universal singular free energy per correlation volume fs2 is equal to -(c12)(2-)(1-)-1, where c is the central charge of the theory at criticality, is the usual specific-heat exponent, and is defined (for >0) in terms of the second moment of the energy correlations.

Abstract: For a general isotropic two-dimensional theory near criticality, the universal singular free energy per correlation volume ${f}_{s}{\ensuremath{\xi}}^{2}$ is equal to $\ensuremath{-}(\frac{c}{12}\ensuremath{\pi})(2\ensuremath{-}\ensuremath{\alpha}){(1\ensuremath{-}\ensuremath{\alpha})}^{\ensuremath{-}1}$, where $c$ is the central charge of the theory at criticality, $\ensuremath{\alpha}$ is the usual specific-heat exponent, and $\ensuremath{\xi}$ is defined (for $\ensuremath{\alpha}g0$) in terms of the second moment of the energy correlations. Some generalizations of this result are also noted.