Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

Finite-size scaling of the free energy levels in the Ising and Potts q=3 universality

Loïc Turban, Jean‐Marc Debierre

Published Apr 21, 1986• 1 citation
Publisher

Abstract

The finite-size scaling of the free energy levels of Privman and Fisher (1984) is tested numerically on two-dimensional lattice strips in the Ising and q=3 Potts universality. The universal amplitudes and the free energy per site are obtained.
DOI
10.1088/0305-4470/19/6/030

Related papers

Universal functions in finite-size scaling: a numerical study in the Ising and Potts q=3 universality class

Jean‐Marc Debierre, Loïc Turban

The universality of the correlation length, order parameter and susceptibility amplitudes is studied in the vicinity of the critical point of two-dimensional models on strips with periodic boundary conditions for the Ising and Potts q=3 universality class. The results confirm Privman-Fisher conjecture (1984).

Journal of Physics A Mathematical and General•May 11, 1987•3 citations

Finite-size scaling corrections in two-dimensional Ising and Potts ferromagnets

Sladequeiroz Instituto De, Potts Ferromagnets

. Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width N sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the `analytical' correction terms, N -2 , are identically zero for triangular and honeycomb Ising systems. For Potts spins, our results are broadly consistent with this lattice-dependent pattern of cancellations, though for correlation lengths non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out. 1. Introduction The systematic study of subdominant terms in scaling provides researchers with guidelines on how to extrapolate, e.g. finite-size results to the thermodynamic limit [1--5]. Also, it may in itself bring out connections to underlying physical properties. These latter may be universal, such as the relationship between critical free-energy finite-width correction and conforma...

•Nov 21, 2007•24 citations

Finite-size scaling corrections in two-dimensional Ising and Potts ferromagnets

S L A de Queiroz

Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width N sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the `analytical' correction terms, N -2 , are identically zero for triangular and honeycomb Ising systems. For Potts spins, our results are broadly consistent with this lattice-dependent pattern of cancellations, though for correlation lengths non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out.

arXiv:cond-mat/9912090•Journal of Physics A Mathematical and General•Jan 24, 2000•27 citations

Universal finite-size scaling amplitudes on a torus for the triangular Ising lattice gas

Hyunggyu Park

Recently the author suggested studying the scaling properties of complex two-dimensional phase transitions by calculating the universal amplitudes of interfacial free energies on a torus geometry employing Monte Carlo simulations. He tests this method at the 3*3 phase transition in the Ising lattice gas on a triangular lattice belonging to the chiral three-state Potts universality class. The interfacial free energies for this lattice gas model can be written in terms of free energy differences between systems with different sizes. The algorithm to calculate these free energy differences is presented. Using lattice sizes up to 18*18 and modest computing effort, he finds that the universal amplitude A=1.220.02, in accordance with the exact analytical value for the non-chiral three-state Potts model, A=1.203291 . . ., which he determined earlier.

Journal of Physics A Mathematical and General•May 21, 1990•2 citations

Universal amplitude of the free energy density in finite-size scaling: the Potts universality

Loïc Turban, Jean‐Marc Debierre

Using the numerical results of the finite-size scaling study of the q-state Potts model by Blote and Nightingale (1982), the authors obtain a conjectured expression for the universal amplitude of the free energy density.

arXiv:cond-mat/0106625•Journal of Physics A Mathematical and General•May 11, 1986•3 citations

Universal finite-size scaling amplitudes of interfacial free energies in Monte Carlo simulations

H Park, Marcel den Nijs

The study of the universal finite-size scaling amplitudes of interfacial free energies in Monte Carlo simulations provides an accurate method of determining the critical temperature and the universality class of phase transitions. These universal amplitudes can replace the critical exponents to identify universality classes. The authors use Bennett's optimisation scheme (1976) for the calculation of the interfacial free energies in Monte Carlo simulations. Tests for the Ising and three-state Potts model confirm the effectiveness of this method.

Journal of Physics A Mathematical and General•Sep 7, 1989•7 citations
. Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width N sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the `analytical' correction terms, N -2 , are identically zero for triangular and honeycomb Ising systems. For Potts spins, our results are broadly consistent with this lattice-dependent pattern of cancellations, though for correlation lengths non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out. 1. Introduction The systematic study of subdominant terms in scaling provides researchers with guidelines on how to extrapolate, e.g. finite-size results to the thermodynamic limit [1--5]. Also, it may in itself bring out connections to underlying physical properties. These latter may be universal, such as the relationship between critical free-energy finite-width correction and conforma...
Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width N sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the `analytical' correction terms, N -2 , are identically zero for triangular and honeycomb Ising systems. For Potts spins, our results are broadly consistent with this lattice-dependent pattern of cancellations, though for correlation lengths non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out.
Recently the author suggested studying the scaling properties of complex two-dimensional phase transitions by calculating the universal amplitudes of interfacial free energies on a torus geometry employing Monte Carlo simulations. He tests this method at the 3*3 phase transition in the Ising lattice gas on a triangular lattice belonging to the chiral three-state Potts universality class. The interfacial free energies for this lattice gas model can be written in terms of free energy differences between systems with different sizes. The algorithm to calculate these free energy differences is presented. Using lattice sizes up to 18*18 and modest computing effort, he finds that the universal amplitude A=1.220.02, in accordance with the exact analytical value for the non-chiral three-state Potts model, A=1.203291 . . ., which he determined earlier.
The study of the universal finite-size scaling amplitudes of interfacial free energies in Monte Carlo simulations provides an accurate method of determining the critical temperature and the universality class of phase transitions. These universal amplitudes can replace the critical exponents to identify universality classes. The authors use Bennett's optimisation scheme (1976) for the calculation of the interfacial free energies in Monte Carlo simulations. Tests for the Ising and three-state Potts model confirm the effectiveness of this method.