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 the Physical Society of Japan

High Temperature Series Expansion of Staggered Susceptibillity of the Three-State Antiferromagnetic Potts Model on d-Dimensional Hypercubic Lattices

Takehiko Oguchi, Haruo Yoshida

Published Apr 15, 1983• 2 citations
Publisher

Abstract

The three-state antiferromagnetic Potts model on d-dimensional hypercubic lattices is studied, where d is 2, 3, 4, 5 and 6. The Hamiltonian is expressed by the spin Hamiltonian with spin 1. The staggered susceptibility is calculated by the high temperature series expansion. By use of the ratio method and the Padé approximation, the critical temperature and the critical exponent γ are obtained. It is concluded that the three-state antiferromagnetic Potts model exhibits the second-order transition when d ≥3.

DOI
10.1143/jpsj.52.1102

Related papers

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

Three-state Potts-model spin glasses on hypercubic lattices

Rajiv R. P. Singh

We develop high-temperature expansions for the Edwards-Anderson susceptibility of the \ifmmode\pm\else\textpm\fi{}J three-state Potts spin glasses on d-dimensional hypercubic lattices. For d\ensuremath{\ge}6, d log Pad\'e approximant analysis yields a second-order phase transition with an exponent \ensuremath{\gamma} consistent with the mean-field value of unity. In lower dimensions the extrapolations are not convergent enough to extract the critical behavior. In d=3, the series are analyzed assuming various finite- and zero-temperature transitions and their consistency with available Monte Carlo data is studied.

Physical review. B, Condensed matter•Mar 1, 1991•11 citations

Series studies of the four-state Potts model

R.V. Ditzian, Leo P. Kadanoff

The four-state Potts model is studied via series expansions. Free energy and susceptibility high-temperature series are calculated for hypercubic lattices of general dimensionality. Estimates of critical temperatures and critical indices gamma and alpha are obtained as functions of dimensionality. The free energy, magnetisation, and susceptibility low-temperature series are calculated for d=4. The high-and low-temperature series together indicate that the phase transition in this dimensionality is first order. From this result the authors suggest that the apparent second-order transitions shown by the susceptibility for d>or=4 might be explained as spinodal pseudotransitions.

Journal of Physics A Mathematical and General•Sep 1, 1979•24 citations

Critical temperature of an anisotropic two-dimensional Potts model

Kaoru Yasumura

The phase transition temperature T c of the q-state Potts model with ferromagnetic interactions J x and antiferromagnetic ones J y in the two respective directions of a 2D lattice is calculated by the high-temperature series expansion (HTSE) of the appropriate staggered susceptibility as well a by the cluster variate approximation (CVA). For q=3 the HTSE result in the range of mod J y mod /J x <or approximately=1.5 shows a good coincidence with the Kosterlitz-Thouless-type phase transition temperature calculated on the prescription by Ostlund which is given by 1/16 pi =exp(-2 beta c J x ) coth(- beta c J y /2), beta =1/kT c . The CVA result shows similar behaviour of T c to that of the Migdal-Kadanoff renormalisation group method obtained by Kinzel et al, but it is considered to be less reliable than the HTSE result.

Journal of Physics A Mathematical and General•Oct 1, 1987•8 citations

High-field series expansions and critical properties for the three-state Potts model

S Mivashita, Donald D. Betts, C. J. Elliott

High-field series expansions are presented for the three-state Potts model on the square, simple cubic and body centred cubic lattices. Estimates of the critical exponents for two dimensions are beta =0.1064+or-0.0005, gamma '=1.50+or-0.04 and delta =15.5+or-1.5. It is plausible that the three-dimensional model undergoes a second-order phase transition with exponents beta =0.203+or-0.004, gamma '=1.18+or-0.05 and delta =7.0+or-0.3.

Journal of Physics A Mathematical and General•Sep 1, 1979•29 citations

High Temperature Series Expansion of the Susceptibility of the d-Dimensional Random Ising Model

Shigeru Okamoto, T. Oguchi, Yohtaro Ueno

The critical temperatures of the random mixtures are investigated in the quenched site and bond Ising model with the ferromagnetic and antiferromagnetic exchange interactions by the high-temperature series expansion of the susceptibility for the d-dimensional simple hypercubical lattices. (d = 2, 3, 4, 5, 6)

Progress of Theoretical Physics•Feb 1, 1982•2 citations
The three-state antiferromagnetic Potts model on d-dimensional hypercubic lattices is studied, where d is 2, 3, 4, 5 and 6. The Hamiltonian is expressed by the spin Hamiltonian with spin 1. The staggered susceptibility is calculated by the high temperature series expansion. By use of the ratio method and the Padé approximation, the critical temperature and the critical exponent γ are obtained. It is concluded that the three-state antiferromagnetic Potts model exhibits the second-order transition when d ≥3.
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.
We develop high-temperature expansions for the Edwards-Anderson susceptibility of the \ifmmode\pm\else\textpm\fi{}J three-state Potts spin glasses on d-dimensional hypercubic lattices. For d\ensuremath{\ge}6, d log Pad\'e approximant analysis yields a second-order phase transition with an exponent \ensuremath{\gamma} consistent with the mean-field value of unity. In lower dimensions the extrapolations are not convergent enough to extract the critical behavior. In d=3, the series are analyzed assuming various finite- and zero-temperature transitions and their consistency with available Monte Carlo data is studied.
The four-state Potts model is studied via series expansions. Free energy and susceptibility high-temperature series are calculated for hypercubic lattices of general dimensionality. Estimates of critical temperatures and critical indices gamma and alpha are obtained as functions of dimensionality. The free energy, magnetisation, and susceptibility low-temperature series are calculated for d=4. The high-and low-temperature series together indicate that the phase transition in this dimensionality is first order. From this result the authors suggest that the apparent second-order transitions shown by the susceptibility for d>or=4 might be explained as spinodal pseudotransitions.
The phase transition temperature T c of the q-state Potts model with ferromagnetic interactions J x and antiferromagnetic ones J y in the two respective directions of a 2D lattice is calculated by the high-temperature series expansion (HTSE) of the appropriate staggered susceptibility as well a by the cluster variate approximation (CVA). For q=3 the HTSE result in the range of mod J y mod /J x <or approximately=1.5 shows a good coincidence with the Kosterlitz-Thouless-type phase transition temperature calculated on the prescription by Ostlund which is given by 1/16 pi =exp(-2 beta c J x ) coth(- beta c J y /2), beta =1/kT c . The CVA result shows similar behaviour of T c to that of the Migdal-Kadanoff renormalisation group method obtained by Kinzel et al, but it is considered to be less reliable than the HTSE result.