Backbone exponents of the two-dimensional q-state Potts model: a Monte Carlo investigation.
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-sqrt[3], 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 P2 of a pair of points connected via at least two independent paths. Finite-size-scaling analysis of P2 yields X(b) as 0.3566(2), 0.2696(3), 0.2105(3), and 0.127(4) for the critical q=2-sqrt[3], 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.
Deng
Youjin
Y
Faculty of Applied Sciences, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
Blöte
Henk W J
HW
Nienhuis
Bernard
B
D000465:Algorithms; D055592:Biophysical Phenomena; D001703:Biophysics; D055598:Chemical Phenomena; D002621:Chemistry; D016000:Cluster Analysis; D005740:Gases; D015233:Models, Statistical; D009010:Monte Carlo Method; D011336:Probability
D005740:Gases