Finite-Size Scaling Study of the Three-State Potts Model in Random Fields: Evidence for a Second-Order Transition

1995 ◽  
Vol 30 (6) ◽  
pp. 331-336 ◽  
Author(s):  
K Eichhorn ◽  
K Binder
Keyword(s):  
Potts Model ◽  
Random Fields ◽  
Finite Size ◽  
Second Order ◽  
Order Transition ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Second Order Transition

Monte Carlo Simulations of Phase Transitions in a Two-Dimensional Random-Bond Potts Model

1996 ◽  
Vol 463 ◽  
Author(s):  
R. Paredes ◽  
J. Valbuena
Keyword(s):  
Potts Model ◽  
Theoretical Calculations ◽  
Finite Size ◽  
Universality Class ◽  
Second Order ◽  
Order Transition ◽  
Scaling Analysis ◽  
Two Dimensional ◽  
Pure Case ◽  
Second Order Transition

ABSTRACTMotivated by recent experiments on phase behavior of systems confined in porous media, we have studied the effect of quenched bond randomness on the nature of the phase transition in the two dimensional Potts model. To model the effects of the porous matrix we chose the couplings of the q state Potts Hamiltonian from the distribution P(Jij) = pδ(Jij – J) + (1 – p)δ(Jij). For a range of p values, away from the percolation threshold, the transition temperature follows the mean field prediction Tc(p) = Tc(1)p. Furthermore, we observed that the strong first order transition, that appears in the pure case for q = 10, changes two a second order transition. It is also clear from our simulations that the second order transition of the q = 3 pure case changes to a second order transition of a different universality class. A finite size scaling analysis suggests that in both cases the critical exponents, in the presence of disorder, fall into the universality class of the two dimensional pure Ising model. This result agrees with theoretical calculations recently published [1].

Finite-size scaling of the three-state Potts model on a simple cubic lattice

1990 ◽  
Vol 59 (5-6) ◽  
pp. 1397-1429 ◽  
Author(s):  
M. Fukugita ◽  
H. Mino ◽  
M. Okawa ◽  
A. Ukawa
Keyword(s):  
Potts Model ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Cubic Lattice ◽  
Size Scaling ◽  
Simple Cubic ◽  
Simple Cubic Lattice

scholarly journals Numerical study on a crossing probability for the four-state Potts model: Logarithmic correction to the finite-size scaling

2019 ◽  
Vol 2019 (9) ◽  
Author(s):  
Kimihiko Fukushima ◽  
Kazumitsu Sakai
Keyword(s):  
Fractal Dimension ◽  
Potts Model ◽  
Scaling Limit ◽  
Finite Size ◽  
Logarithmic Correction ◽  
Finite Size Scaling ◽  
Spin Cluster ◽  
Size Scaling ◽  
Aspect Ratios ◽  
Crossing Probability

Abstract A crossing probability for the critical four-state Potts model on an $L\times M$ rectangle on a square lattice is numerically studied. The crossing probability here denotes the probability that spin clusters cross from one side of the boundary to the other. First, by employing a Monte Carlo method, we calculate the fractal dimension of a spin cluster interface with a fluctuating boundary condition. By comparison of the fractal dimension with that of the Schramm–Loewner evolution (SLE), we numerically confirm that the interface can be described by the SLE with $\kappa=4$, as predicted in the scaling limit. Then, we compute the crossing probability of this spin cluster interface for various system sizes and aspect ratios. Furthermore, comparing with the analytical results for the scaling limit, which have been previously obtained by a combination of the SLE and conformal field theory, we numerically find that the crossing probability exhibits a logarithmic correction ${\sim} 1/\log(L M)$ to the finite-size scaling.

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