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 Nuclear and General

Critical polarization of the eight-vertex model

Ian Graham Enting, David S. Gaunt

Published Mar 21, 1974• 9 citations
Publisher

Abstract

Investigating by series analysis the polarization of the eight-vertex model as a function of electric field at T c and zero magnetic field, estimates of the exponent delta e are obtained. These estimates are combined with a conjectured scaling relation to give a simple prediction for the spontaneous polarization exponent beta e .
DOI
10.1088/0305-4470/7/5/004

Related papers

Spontaneous polarization of the eight-vertex model

R. J. Baxter, S B Kelland

A functional form of the spontaneous polarization P 0 of the eight-vertex model below the critical temperature is conjectured, and an exact expression then determined by considering three special cases. The result agrees to fourth order with the low-temperature series expansion. It implies that the critical exponent beta e varies linearly with pi /$Gm, as do the other exponents previously obtained.

Journal of Physics C Solid State Physics•Nov 21, 1974•49 citations

On the spontaneous order of the eight-vertex model

Michael N. Barber, R. J. Baxter

A functional form for the spontaneous order M 0 of the eight-vertex model is conjectured from an investigation of the structure of a low-temperature expansion of M 0 . The precise expression then follows from the known result for the Ising case. The exponent beta is then obtained and three-exponent scaling used to predict the remaining exponents of the eight-vertex model from the known exponents.

Journal of Physics C Solid State Physics•Oct 16, 1973•71 citations

Relations for polarization exponents (in magnetic lattice theory)

Ian Graham Enting

It is pointed out that the eight-vertex model, the triplet model and the Ashkin-Teller (1943) model have a common exponent relation beta e = 1 / 4 - 1 / 4 alpha that is not a consequence of scaling theory. It is proposed that this relation reflects a special symmetry of these models and this proposal is related to possible classification of two-dimensional systems.

Journal of Physics A Mathematical and General•Oct 1, 1975•11 citations

Magnetic exponents of the two-dimensional q-state Potts model

Bernard Nienhuis, Eberhard K. Riedel, Michael Schick C

The results of a variational renormalisation-group calculation for the magnetic exponent y H of the two-dimensional q-state Potts model suggest a simple relationship between y H and the exactly known critical exponent y T 8v of the eight-vertex model. The relation allows one to predict the critical and tricritical magnetic exponent delta of the q-state Potts model as a function of q.

Journal of Physics A Mathematical and General•Jun 1, 1980•236 citations

A PHASE TRANSITION MODEL NOT IN ACCORDANCE WITH THE SCALING LAW

SUN XIN, 复旦大学物理系

For a three-dimensional eight-vertex model with energy parameters satisfying the condition ε1+ε2=ε3+ε4, all the critical exponents have been calculated:α=α′=0,β=1/4,δ=7,γ=1/2,γ′=3/2,ν=ν′=1,η=3/2. These do not satisfy the scaling law, the reason is that the correlative region of polarization contracts from the crystal planes (1, 1, 1) and (1, 1, 1) to the crystal axis [1, 0, 1] at the critical point.

Acta Physica Sinica•Jan 1, 1976•0 citations

Critical exponents of the modified F model

Herm Jan Brascamp, H Kunz, Fa Yueh Wu

Critical exponents of an eight-vertex model, the modified F model, are obtained. The results beta = 1 / 4 , gamma = gamma '= 3 / 2 , eta = 1 / 2 , nu = nu '=1 together with the established indices alpha = alpha '=0 obey the scaling relations.

Journal of Physics C Solid State Physics•Apr 12, 1973•11 citations