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 C Solid State Physics

Transition temperature in a new integral representation for the Ising ferromagnet

B. Frank, O Mitran

Published Sep 14, 1978• 0 citations
Publisher
DOI
10.1088/0022-3719/11/17/525

Related papers

New integral representation for the spin S Ising ferromagnet

B. Frank, O Mitran

Solid State Communications•Mar 1, 1978•11 citations

Integral representation for the spin Ising ferromagnet

B. Frank, O Mitran

Solid State Communications•Oct 1, 1977•14 citations

Transition temperature of an Ising ferromagnet

A. Ojo

Physics Letters A•Oct 1, 1973•7 citations

Phase transition in a two-dimensional Ising ferromagnet based on the generalized zero-temperature Glauber dynamics

孟庆宽, 冯东太, 高绪团 +1 more

中国物理B：英文版•Jan 1, 2013•0 citations

Critical exponents in a new integral representation for the Ising ferromagnet

B. Frank

The rational values beta = 5 / 16 , delta =5, alpha = 1 / 8 , nu = 5 / 8 , and eta =0 of the critical exponents for the three-dimensional spin 1 / 2 Ising ferromagnet are shown to be consistent with a recently-derived linearised equation for the Ising two-spin correlation function. This equation arises from an exact integral representation which previously, on application of a straightforward approximation for higher-order cumulant averages, was shown to yield transition temperatures T c to within 2% of their correct values for the cubic lattices. In the search for beta , the requirement is imposed that the correction terms for the magnetisation and for M 2 , a quantity closely related to the system internal energy, be analytic in some power of T c -T (which turns out to be 1 / 8 ) when the external magnetic field h is zero.

Journal of Physics C Solid State Physics•May 28, 1978•9 citations

Transition temperature in a new integral representation for the Ising ferromagnet

B. Frank, O Mitran

An infinite set of coupled integral equations is found, with the use of a spectral theorem for the correlation functions of the spin-1/2 three-dimensional Ising model. The second equation is linearised to yield the two spin correlation function. The Ward identity is then satisfied. Those approximations which give the Weiss and spherical model results are indicated. The transition temperature is calculated for SC, BCC and FCC lattices using a product average decomposition of the higher-order correlation functions. The scheme is seen to converge toward the respective values 0.738, 0.789 and 0.823 of 4/ beta c J(0) which are within 2% of the exact values 0.752, 0.794 and 0.816.

Journal of Physics C Solid State Physics•Jul 28, 1977•37 citations
The rational values beta = 5 / 16 , delta =5, alpha = 1 / 8 , nu = 5 / 8 , and eta =0 of the critical exponents for the three-dimensional spin 1 / 2 Ising ferromagnet are shown to be consistent with a recently-derived linearised equation for the Ising two-spin correlation function. This equation arises from an exact integral representation which previously, on application of a straightforward approximation for higher-order cumulant averages, was shown to yield transition temperatures T c to within 2% of their correct values for the cubic lattices. In the search for beta , the requirement is imposed that the correction terms for the magnetisation and for M 2 , a quantity closely related to the system internal energy, be analytic in some power of T c -T (which turns out to be 1 / 8 ) when the external magnetic field h is zero.
An infinite set of coupled integral equations is found, with the use of a spectral theorem for the correlation functions of the spin-1/2 three-dimensional Ising model. The second equation is linearised to yield the two spin correlation function. The Ward identity is then satisfied. Those approximations which give the Weiss and spherical model results are indicated. The transition temperature is calculated for SC, BCC and FCC lattices using a product average decomposition of the higher-order correlation functions. The scheme is seen to converge toward the respective values 0.738, 0.789 and 0.823 of 4/ beta c J(0) which are within 2% of the exact values 0.752, 0.794 and 0.816.