We compute the 2n-point renormalized coupling constants in the symmetric phase of the three-dimensional (3D) Ising model on the simple cubic lattice in terms of the high temperature expansions O(${\mathrm{\ensuremath{\mathrm{B}}}}^{17}$) of the Fourier transformed 2n-point connected correlation functions at zero momentum. Our high temperature estimates of these quantities, which enter into the small field expansion of the effective potential for a 3D scalar field at the infrared fixed point or, equivalently, in the critical equation of state of the 3D Ising model universality class, are compared with recent results obtained by renormalization group methods, strong coupling, stochastic simulations, as well as previous high temperature expansions.We compute the 2n-point renormalized coupling constants in the symmetric phase of the three-dimensional (3D) Ising model on the simple cubic lattice in terms of the high temperature expansions O(${\mathrm{\ensuremath{\mathrm{B}}}}^{17}$) of the Fourier transformed 2n-point connected correlation functions at zero momentum. Our high temperature estimates of these quantities, which enter into the small field expansion of the effective potential for a 3D scalar field at the infrared fixed point or, equivalently, in the critical equation of state of the 3D Ising model universality class, are compared with recent results obtained by renormalization group methods, strong coupling, stochastic simulations, as well as previous high temperature expansions.

arXiv:hep-lat/9703017Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJun 1, 199740 citations

Higher-order interactions in the linear ising model

I. S. Donskaya

Theoretical and Mathematical PhysicsMar 1, 19881 citation

Strong-coupling expansions for multidimensional Ising and O(n) spin systems

Gerald E. Sobelman

Recent lattice Hamiltonian strong-coupling calculations for the (1+1)-dimensional Ising, O(2), O(3), and O(4) models are extended to $d+1$ dimensions and to general $\mathrm{O}(n)$ symmetry. This allows a nontrivial numerical check on the rate of convergence of the strong-coupling expansions as the multidimensional models all have standard second-order phase transitions which have been well studied by other methods. Dlog-Pad\'e analysis of the fourth-order mass gap series for the (2+1)-dimensional Ising model show the critical exponent $\ensuremath{\nu}$ to be calculated to about the 10% level of accuracy. The behavior of $\ensuremath{\nu}$ as a function of $d$ and $n$ is exhibited and compared against known results. Mean-field behavior is recovered exactly in the $d\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, while the Berlin-Kac spherical model is obtained in the $n\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.Recent lattice Hamiltonian strong-coupling calculations for the (1+1)-dimensional Ising, O(2), O(3), and O(4) models are extended to $d+1$ dimensions and to general $\mathrm{O}(n)$ symmetry. This allows a nontrivial numerical check on the rate of convergence of the strong-coupling expansions as the multidimensional models all have standard second-order phase transitions which have been well studied by other methods. Dlog-Pad\'e analysis of the fourth-order mass gap series for the (2+1)-dimensional Ising model show the critical exponent $\ensuremath{\nu}$ to be calculated to about the 10% level of accuracy. The behavior of $\ensuremath{\nu}$ as a function of $d$ and $n$ is exhibited and compared against known results. Mean-field behavior is recovered exactly in the $d\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, while the Berlin-Kac spherical model is obtained in the $n\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.

Physical review. B, Condensed matterAug 1, 19813 citations

A simple approximation for Ising spin models

Hadey K. Mohamad

Chinese Journal of PhysicsJun 15, 20181 citation

Critical properties of an S=1 multispin coupling Ising model

Ferenc Iglói, D. Kapor, M. J. Škrinjaŕ

Strong and weak coupling series expansions are used to investigate the critical properties of the S=1 multispin coupling Ising chain in the presence of a transverse field. The order of the transition goes from second order to first order when more than three spins are coupled. According to the numerical results the two-spin and three-spin coupling models belong to the Ising and the four-state Potts universality classes, respectively. Thus the critical properties of the model do not depend on the value of the spin, even when three spins are coupled.Strong and weak coupling series expansions are used to investigate the critical properties of the S=1 multispin coupling Ising chain in the presence of a transverse field. The order of the transition goes from second order to first order when more than three spins are coupled. According to the numerical results the two-spin and three-spin coupling models belong to the Ising and the four-state Potts universality classes, respectively. Thus the critical properties of the model do not depend on the value of the spin, even when three spins are coupled.

Journal of Physics A Mathematical and GeneralMar 11, 19872 citations

Recent lattice Hamiltonian strong-coupling calculations for the (1+1)-dimensional Ising, O(2), O(3), and O(4) models are extended to

d+1

dimensions and to general

\mathrm{O}(n)

symmetry. This allows a nontrivial numerical check on the rate of convergence of the strong-coupling expansions as the multidimensional models all have standard second-order phase transitions which have been well studied by other methods. Dlog-Pad\'e analysis of the fourth-order mass gap series for the (2+1)-dimensional Ising model show the critical exponent $\ensuremath{\nu}$ to be calculated to about the 10% level of accuracy. The behavior of $\ensuremath{\nu}$ as a function of

d

and

n

is exhibited and compared against known results. Mean-field behavior is recovered exactly in the $d\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, while the Berlin-Kac spherical model is obtained in the $n\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.