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

physica status solidi (b)

One Possible Analytical Approximation of the Critical Point of the Three‐Dimensional Ising Model

András Szász

Published Aug 1, 1985• 1 citation
Publisher
DOI
10.1002/pssb.2221300250

Related papers

Padé approximations and the critical exponents in the two- and three-dimensional Ising models

Paul H. E. Meijer, Richard A. Farrell

Pad\'e approximants have been used to estimate both the critical temperature and the critical-point exponents of the Ising model. In the standard Pad\'e analysis the approximants near the diagonal are given more credence. In the present study of two-dimensional models more credence is given to those entries for which the estimated critical temperature is close to the exact value. For three-dimensional models an analogous method is employed using the "exact" critical temperature estimated from the high-temperature compressibility series. The rationale for selecting these particular approximants is based on the fact that one is estimating critical-point behavior by extrapolating from a series representation. Thus, if the estimated critical point is shifted from its true value, one should expect a corresponding shift in the estimated exponent. Indeed, this is what is found.

Physical review. B, Solid state•Jul 1, 1975•9 citations

Behaviour of the Finite-Sized, Three-Dimensional, Ising Model Near the Critical Point

George Allen Baker Jr., Rajan Gupta

Springer proceedings in physics•Jan 1, 1997•0 citations

On the renormalization group fixed point of the two-dimensional Ising model at criticality

Alexander Stottmeister, Tobias J. Osborne

We analyze the renormalization group fixed point of the two-dimensional Ising model at criticality. In contrast with expectations from tensor network renormalization (TNR), we show that a simple, explicit analytic description of this fixed point using operator-algebraic renormalization (OAR) is possible. Specifically, the fixed point is characterized in terms of spin-spin correlation functions. Explicit error bounds for the approximation of continuum correlation functions are given.

Scientific Reports•Sep 8, 2023•3 citations

Dynamics of the Ising Model near the Critical Point

Masuo Suzuki, 英雄 猪狩

•Jul 20, 1968•0 citations

Subdominant critical indices for the ferromagnetic susceptibility of the spin-1/2 Ising model

D. Bessis, Pierre Moussa, Giorgio Turchetti

Starting from the high-temperature series for the susceptibility of the spin- 1 / 2 ferromagnetic Ising models-square, planar triangular, SC, BCC, FCC, diamond, and HSC in four, five and six dimensions-the authors analyse the analytical structure near the critical point of the susceptibility by writing it as a Laplace transform in the variable log (1-w/w c ), where w=tanh( beta J). The interest of the method is that the coalescing singularities which sit at w=w c are spread out and can be analysed separately, the first subdominant critical indices, appearing as stable poles of Pade approximants. They first recover the results for the two-dimensional models, with a high accuracy: gamma =1.74995 and gamma s =0.757. The most stable results in three dimensions are obtained for the diamond lattice: gamma =1.2506+or-0.0015 and gamma s =0.42+or-0.11. The other lattices give 0.10< gamma s <0.52. However, in all three-dimensional cases the amplitude of the subdominant singularity is less than a few per cent of the leading one. Therefore the uncertainties are large, but the subdominant singularity stays closer to the value Gamma -1=0.25 than to the field theoretical predicted one gamma s =0.75.

Journal of Physics A Mathematical and General•Aug 1, 1980•8 citations

The dynamic critical exponent of the three-dimensional Ising model

R. Matz, D. L. Hunter, Naeem Jan

Journal of Statistical Physics•Feb 1, 1994•34 citations
Pad\'e approximants have been used to estimate both the critical temperature and the critical-point exponents of the Ising model. In the standard Pad\'e analysis the approximants near the diagonal are given more credence. In the present study of two-dimensional models more credence is given to those entries for which the estimated critical temperature is close to the exact value. For three-dimensional models an analogous method is employed using the "exact" critical temperature estimated from the high-temperature compressibility series. The rationale for selecting these particular approximants is based on the fact that one is estimating critical-point behavior by extrapolating from a series representation. Thus, if the estimated critical point is shifted from its true value, one should expect a corresponding shift in the estimated exponent. Indeed, this is what is found.
Starting from the high-temperature series for the susceptibility of the spin- 1 / 2 ferromagnetic Ising models-square, planar triangular, SC, BCC, FCC, diamond, and HSC in four, five and six dimensions-the authors analyse the analytical structure near the critical point of the susceptibility by writing it as a Laplace transform in the variable log (1-w/w c ), where w=tanh( beta J). The interest of the method is that the coalescing singularities which sit at w=w c are spread out and can be analysed separately, the first subdominant critical indices, appearing as stable poles of Pade approximants. They first recover the results for the two-dimensional models, with a high accuracy: gamma =1.74995 and gamma s =0.757. The most stable results in three dimensions are obtained for the diamond lattice: gamma =1.2506+or-0.0015 and gamma s =0.42+or-0.11. The other lattices give 0.10< gamma s <0.52. However, in all three-dimensional cases the amplitude of the subdominant singularity is less than a few per cent of the leading one. Therefore the uncertainties are large, but the subdominant singularity stays closer to the value Gamma -1=0.25 than to the field theoretical predicted one gamma s =0.75.