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 de physique

Quantum Hamiltonian formulation of the q-state Potts model : weak-coupling expansion

Loïc Turban

Published Jan 1, 1981• 2 citations
Publisher

Abstract

A one-dimensional quantum formulation of the two-dimensional q-state Potts model is studied using a weak-coupling perturbation expansion for the ground state energy. The series for the spontaneous magnetization, the susceptibility and the specific heat are analysed using the method of Padé approximants. The critical exponents, interpolated to the exact value of the critical coupling, are in good agreement with the conjectures of den Nijs, Alexander and Enting for q = 3 and q = 4.

DOI
10.1051/jphys:01981004206079300

Related papers

Critical exponents of two-dimensional Potts and bond percolation models

Henk W. J. Blöte, M. P. Nightingale, Bernard Derrida

Critical exponents of the two-dimensional, q-state Potts model are calculated by means of finite size scaling and transfer matrix techniques for continuous q. Results for the temperature exponent agree accurately with the conjecture of den Nijs (1979). The magnetic exponent is found to behave in accordance with the conjecture of Nienhuis et al. (1980).

Journal of Physics A Mathematical and General•Feb 1, 1981•85 citations

Thermal critical exponents of the q -state Potts model

Murray T. Batchelor

This Viewpoint relates to an article by den Nijs (1979 J. Phys. A: Math. Gen. 12 1857) and was published as part of a series of Viewpoints celebrating 50 of the most influential papers published in the J. Phys. series, which is celebrating its 50th anniversary. In this landmark paper Marcel den Nijs, at that time a graduate student supervised by Hubert Knops in Nijmegen, The Netherlands, proposed an exact formula for the thermal critical exponents of the two-dimensional q-state Potts model. The enduring influence of this paper is a measure of the importance of the Potts model and the value of exact results

Journal of Physics A Mathematical and Theoretical•Mar 3, 2017•1 citation

High Temperature Series Expansion of the d-Dimensional q-State Antiferromagnetic Potts Model

Kaoru Yasumura, Takehiko Oguchi

High temperature series expansions of the staggered susceptibility of the q -state antiferromagnetic Potts model (AFPM) on a d -dimensional hypercubic lattice are calculated. For arbitrary values of q and d , the transition temperatures and the critical exponents γ are determined by use of the ratio method and the Padé approximation. It is shown that the 3- and 4-state AFPM exhibit a second-order phase transition when d ≥3, and the 5- and 6-state AFPM do when d ≥4, etc. In the limit of infinite d , the transition temperature T c is obtained rigorously as k T c / J ={log [2 d /(2 d - q )]} -1 ( k : the Boltzmann constant, J : the interaction parameter), and the ordered phase exists when d > q /2.

Journal of the Physical Society of Japan•Feb 1, 1984•9 citations

A study of logarithmic corrections and universal amplitude ratios in the two-dimensional 4-state Potts model

Щур Лев Николаевич, Bertrand Berche, P. Butera

Monte Carlo (MC) and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the two-dimensional 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic corrections is discussed and an approach is proposed in order to account numerically for these corrections in the determination of critical amplitudes. Accurate estimates of universal amplitude ratios A + / A - , Γ + /Γ - , Γ T /Γ - and R C ± are given, which arouse new questions with respect to previous works.

arXiv:0707.2430•Europhysics Letters (EPL)•Jan 3, 2008•10 citations

Series studies of the Potts model. I. The simple cubic Ising model

A J Guttmann, I G Enting

The finite-lattice method of series expansion is generalized to the q-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained, unlike two-dimensional lattices where the computational requirements grow exponentially with the number of terms. For the Ising (q=2) case the authors have extended the low-temperature series for the partition functions, magnetization and zero-field susceptibility to u 26 from u 20 . The high-temperature series for the zero-field partition function is extended from nu 18 to nu 22 . Subsequent analysis gives critical exponents in agreement with those from field theory.

arXiv:hep-lat/9212032•Journal of Physics A Mathematical and General•Feb 21, 1993•49 citations

Large- q expansion of the specific heat for the two-dimensionalq-state Potts model

H. Arisue, Kanehito Tabata

We have calculated the large-$q$ expansion for the specific heat at the phase transition point in the two-dimensional q-state Potts model to the 23rd order in $1/\sqrt{q}$ using the finite lattice method. The series obtained allows us to give highly convergent estimates of the specific heat for $q>4$ on the first-order transition point. The result confirms the correctness of the conjecture by Bhattacharya et al. [Nucl. Phys. B 435, 526 (1995); J. Phys. I 7, 1155 (1997)] on the asymptotic behavior of the specific heat for $\stackrel{\ensuremath{\rightarrow}}{q}4.$

arXiv:hep-lat/9807005•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jan 1, 1999•8 citations
A one-dimensional quantum formulation of the two-dimensional q-state Potts model is studied using a weak-coupling perturbation expansion for the ground state energy. The series for the spontaneous magnetization, the susceptibility and the specific heat are analysed using the method of Padé approximants. The critical exponents, interpolated to the exact value of the critical coupling, are in good agreement with the conjectures of den Nijs, Alexander and Enting for q = 3 and q = 4.
This Viewpoint relates to an article by den Nijs (1979 J. Phys. A: Math. Gen. 12 1857) and was published as part of a series of Viewpoints celebrating 50 of the most influential papers published in the J. Phys. series, which is celebrating its 50th anniversary. In this landmark paper Marcel den Nijs, at that time a graduate student supervised by Hubert Knops in Nijmegen, The Netherlands, proposed an exact formula for the thermal critical exponents of the two-dimensional q-state Potts model. The enduring influence of this paper is a measure of the importance of the Potts model and the value of exact results
High temperature series expansions of the staggered susceptibility of the q -state antiferromagnetic Potts model (AFPM) on a d -dimensional hypercubic lattice are calculated. For arbitrary values of q and d , the transition temperatures and the critical exponents γ are determined by use of the ratio method and the Padé approximation. It is shown that the 3- and 4-state AFPM exhibit a second-order phase transition when d ≥3, and the 5- and 6-state AFPM do when d ≥4, etc. In the limit of infinite d , the transition temperature T c is obtained rigorously as k T c / J ={log [2 d /(2 d - q )]} -1 ( k : the Boltzmann constant, J : the interaction parameter), and the ordered phase exists when d > q /2.
Monte Carlo (MC) and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the two-dimensional 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic corrections is discussed and an approach is proposed in order to account numerically for these corrections in the determination of critical amplitudes. Accurate estimates of universal amplitude ratios A + / A - , Γ + /Γ - , Γ T /Γ - and R C ± are given, which arouse new questions with respect to previous works.
The finite-lattice method of series expansion is generalized to the q-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained, unlike two-dimensional lattices where the computational requirements grow exponentially with the number of terms. For the Ising (q=2) case the authors have extended the low-temperature series for the partition functions, magnetization and zero-field susceptibility to u 26 from u 20 . The high-temperature series for the zero-field partition function is extended from nu 18 to nu 22 . Subsequent analysis gives critical exponents in agreement with those from field theory.
We have calculated the large-qqq expansion for the specific heat at the phase transition point in the two-dimensional q-state Potts model to the 23rd order in 1/q1/\sqrt{q}1/q​ using the finite lattice method. The series obtained allows us to give highly convergent estimates of the specific heat for q>4q>4q>4 on the first-order transition point. The result confirms the correctness of the conjecture by Bhattacharya et al. [Nucl. Phys. B 435, 526 (1995); J. Phys. I 7, 1155 (1997)] on the asymptotic behavior of the specific heat for $\stackrel{\ensuremath{\rightarrow}}{q}4.$