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

The high-temperature susceptibility of the q-state Potts model behaves as Γ|T − Tc| as T → Tc+, while for T → Tc− one may define both longitudinal and transverse susceptibilities, with the same power law but different amplitudes ΓL and ΓT . We extend a previous analytic calculation of the universal ratio Γ/ΓL in two dimensions to the low-temperature ratio ΓT /ΓL, 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 ΓT /ΓL, but not with that for Γ/ΓL. 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 Γ/ΓL, and our work suggests that these may be unjustified.