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.
Faculty of Applied Sciences, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
Youjin
Y
Deng
Henk W J
HW
Blöte
Bernard
B
Nienhuis
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