SCALAR SUSCEPTIBILITY IN QCD AND THE MULTIFLAVOR SCHWINGER MODEL

We evaluate the leading infrared behavior of the scalar susceptibility in QCD and in the multiflavor Schwinger model for a small nonzero qua rk mass rn and/or small nonzero temperature as well as the scalar susc eptibility for the finite-volume QCD partition function. In QCD, it is determined by one-loop chiral perturbation theory, with the result th at the leading infrared singularity behaves as similar to ln m at zero temperature and as similar to T/root m at finite temperature. In the Schwinger model with several flavors we use exact results for the scal ar correlation function. We find that the Schwinger model has a phase transition at T=0 with critical exponents that satisfy the standard sc aling relations. The singular behavior of this model depends on the nu mber of flavors with a scalar susceptibility that behaves as similar t o m(-2/(Nf+1))). At finite volumes V we show that the scalar susceptib ility is proportional to 1/m(2)V. Recent lattice calculations of this quantity by Karsch and Laermann are discussed.