Backbone exponents of the two-dimensional q-state Potts model:: A Monte Carlo investigation -: art. no. 026114

We determine the backbone exponent X-b of several critical and tricritical q-state Potts models in two dimensions. The critical systems include the bond percolation, the Ising, the q=2-root3, 3, and 4 state Potts, and the Baxter-Wu model, and the tricritical ones include the q=1 Potts model and the Blume-Capel model. For this purpose, we formulate several efficient Monte Carlo methods and sample the probability P-2 of a pair of points connected via at least two independent paths. Finite-size-scaling analysis of P-2 yields X-b as 0.3566(2), 0.2696(3), 0.2105(3), and 0.127(4) for the critical q=2-root3, 1,2, 3, and 4 state Potts model, respectively. At tricriticality, we obtain X-b=0.0520(3) and 0.0753(6) for the q=1 and 2 Potts model, respectively. For the critical q-->0 Potts model it is derived that X-b=3/4. From a scaling argument, we find that, at tricriticality, X-b reduces to the magnetic exponent, as confirmed by the numerical results.