Susceptibility amplitude ratios in the two-dimensional Potts model and percolation

The high-temperature susceptibility of the q-state Potts model behaves as Gamma\T- T-c\(-gamma) as T --> T-c + while for T --> T-c - one may define both longitudinal and transverse susceptibilities, with the same power law but different amplitudes Gamma(L) and Gamma(T). We extend a previous analytic calculation of the universal ratio Gamma/Gamma(L) in two dimensions to the low-temperature ratio Gamma(T)/Gamma(L), and test both predictions with Monte Carlo simulations for q = 3 and 4. The data for q = 4 are inconclusive owing to large corrections to scaling, while for q = 3 they appear consistent with the prediction for Gamma(T)/Gamma(L), but not with that for Gamma/Gamma(L). A simple extrapolation of our analytic results to q --> 1 indicates a similar discrepancy with the corresponding measured quantities in percolation. We point out that stronger assumptions were made in the derivation of the ratio Gamma/Gamma(L), and our work suggests that these may be unjustified. (C) 2000 Elsevier Science B.V. All rights reserved.