scholarly journals Finite-size scaling for first-order transitions: Potts model

1995 ◽  
Vol 80 (5-6) ◽  
pp. 1433-1442 ◽  
Author(s):  
P. M. C. de Oliveira ◽  
S. M. Moss de Oliveira ◽  
C. E. Cordeiro ◽  
D. Stauffer
Keyword(s):  
Potts Model ◽  
Finite Size ◽  
Finite Size Scaling ◽  
First Order ◽  
Size Scaling

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 Transmuted Finite-size Scaling at First-order Phase Transitions

2014 ◽  
Vol 57 ◽  
pp. 68-72 ◽  
Author(s):  
Marco Mueller ◽  
Wolfhard Janke ◽  
Desmond A. Johnston
Keyword(s):  
Phase Transitions ◽  
Finite Size ◽  
Finite Size Scaling ◽  
First Order ◽  
Size Scaling ◽  
First Order Phase

A MICROSCOPIC THEORY OF FINITE-SIZE SCALING

1992 ◽  
Vol 03 (05) ◽  
pp. 897-912 ◽  
Author(s):  
CHRISTIAN BORGS
Keyword(s):  
Finite Size ◽  
Microscopic Theory ◽  
Finite Size Scaling ◽  
Rigorous Theory ◽  
First Order ◽  
Mathematical Proofs ◽  
Mass Gap ◽  
Size Scaling ◽  
Main Emphasis ◽  
Cubic Systems

In this paper, I give an overview over a recently developed rigorous theory of finite-size scaling near first order transitions. Leaving out details of the mathematical proofs, the main emphasis is put on the underlying physical ideas and the discussion of the validity of the results for regions which are, in the sense of mathematical rigour, not covered by the original papers. I present both the finite-size scaling for cubic systems and for long cylinders, discussing also a recent controversy which stems from our work on the finite-size scaling of the mass gap in long cylinders.

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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