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

The high-temperature susceptibility of the q-state Potts model behaves as Γ|T−Tc|−γ 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.