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We present a numerical study of the self-affine profiles obtained fromconfigurations of the q-state Potts (with q=2,3 and 7) and p=10 clock models aswell as from the occupation states for site-percolation on the square lattice.The first and second order static phase transitions of the Potts model arelocated by a sharp change in the value of the roughness exponent $\alpha$characterizing those profiles. The low temperature phase of the Potts modelcorresponds to flat ($\alpha\simeq 1$) profiles, whereas its high temperaturephase is associated to rough ($\alpha\simeq 0.5$) ones. For the p=10 clockmodel, in addition to the flat (ferromagnetic) and rough (paramagnetic)profiles, an intermediate rough ($0.5< \alpha <1$) phase - associated to a softspin-wave one - is observed. Our results for the transition temperatures in thePotts and clock models are in agreement with the static values, showing thatthis approach is able to detect the phase transitions in these models directlyfrom the spin configurations, without any reference to thermodynamicalpotentials, order parameters or response functions. Finally, we show that theroughness exponent $\alpha$ is insensitive to geometric critical phenomena.Comment: 8 pages, 9 figures, submitted to Phys. Rev.

Roughness exponent in two-dimensional percolation, Potts model, and clock model