An alternative approach is proposed to treat the critical point for general Ising spin systems. From the analytic properties of the free energy, we are in principle able to calculate analytically the critical temperature ${\mathit{T}}_{\mathit{c}}$ (l) for (d+1)-dimensional Ising films to any order cumulant as a function of the number l of hyperlayers in the hyperfilm. Explicit expressions up to the fourth order are given. It is shown from the general expression for ${\mathit{T}}_{\mathit{c}}^{(\mathit{m})}$ (l) that [ ${\mathit{T}}_{\mathit{c}}$ (l)- ${\mathit{T}}_{\mathit{c}}$ ]/ ${\mathit{T}}_{\mathit{c}}$ =b/(l+a) in the limit l\ensuremath{\rightarrow}\ensuremath{\infty}. Comparisons with existing results for d=2 are discussed.An alternative approach is proposed to treat the critical point for general Ising spin systems. From the analytic properties of the free energy, we are in principle able to calculate analytically the critical temperature ${\mathit{T}}_{\mathit{c}}$(l) for (d+1)-dimensional Ising films to any order cumulant as a function of the number l of hyperlayers in the hyperfilm. Explicit expressions up to the fourth order are given. It is shown from the general expression for ${\mathit{T}}_{\mathit{c}}^{(\mathit{m})}$(l) that [${\mathit{T}}_{\mathit{c}}$(l)-${\mathit{T}}_{\mathit{c}}$]/${\mathit{T}}_{\mathit{c}}$=b/(l+a) in the limit l\ensuremath{\rightarrow}\ensuremath{\infty}. Comparisons with existing results for d=2 are discussed.

Physical Review AAug 1, 199226 citations

Quantum critical phenomena in spin systems

Subir Sachdev A

Jan 1, 19970 citations

Generalization of the Curie-Weiss Model to the D-dimensional Spin System

Hyung-june Woo, Eun Kyung Lee, Eok-Kyun Lee

The critical behavior of the classical D-dimensional spin model (D2), which is intermediate model that link up the Ising (D = 1) and the spherical model (D = ), is studied for the case of constant coupling interaction independent of the spin-spin distance (Curie-Weiss model). Analytical results show that the critical behavior of the present model is in quantitative agreement with the prediction of the phenomenological mean-field theory independent of D. Critical temperature is calculated to be T=k/JD. This gives a quantitative explanation of the relationship between the spin degree of freedom and the critical temperature.The critical behavior of the classical D-dimensional spin model (D2), which is intermediate model that link up the Ising (D = 1) and the spherical model (D = ), is studied for the case of constant coupling interaction independent of the spin-spin distance (Curie-Weiss model). Analytical results show that the critical behavior of the present model is in quantitative agreement with the prediction of the phenomenological mean-field theory independent of D. Critical temperature is calculated to be T=k/JD. This gives a quantitative explanation of the relationship between the spin degree of freedom and the critical temperature.

Bulletin of the Korean Chemical SocietyAug 1, 19930 citations

Critical temperature of Ising films with cubic lattices

D. L. Lin, Hao Che, Wei Lai +1 more

Following the approach recently proposed by Lin, Che, and Xia [Phys. Rev. A 46, 1805 (1992)], we calculate the critical temperature ${\mathit{T}}_{\mathit{c}}$ for Ising films with lattice structures other than simple cubic by means of the variational cumulant expansion (VCE) of the free energy of the spin system. The critical temperature is derived in terms of the ratio of two successive cumulants to an arbitrary order of accuracy. Since the cumulant of any order m can be calculated analytically by a graphic method, analytical expressions of ${\mathit{T}}_{\mathit{c}}$ can be derived, in principle, as functions of the number L of spin layers in the film to an arbitrary order of accuracy in the VCE. We describe the graphic method in great detail in this paper, and calculate ${\mathit{T}}_{\mathit{c}}$ up to the fourth-order cumulant for films of body-centered-cubic lattice and to the third order for films of face-centered-cubic lattice. Our results show that in the limit of L\ensuremath{\rightarrow}\ensuremath{\infty}, ${\mathit{T}}_{\mathit{c}}$ approaches the corresponding bulk value rather quickly with increasing m in both cases.Following the approach recently proposed by Lin, Che, and Xia [Phys. Rev. A 46, 1805 (1992)], we calculate the critical temperature ${\mathit{T}}_{\mathit{c}}$ for Ising films with lattice structures other than simple cubic by means of the variational cumulant expansion (VCE) of the free energy of the spin system. The critical temperature is derived in terms of the ratio of two successive cumulants to an arbitrary order of accuracy. Since the cumulant of any order m can be calculated analytically by a graphic method, analytical expressions of ${\mathit{T}}_{\mathit{c}}$ can be derived, in principle, as functions of the number L of spin layers in the film to an arbitrary order of accuracy in the VCE. We describe the graphic method in great detail in this paper, and calculate ${\mathit{T}}_{\mathit{c}}$ up to the fourth-order cumulant for films of body-centered-cubic lattice and to the third order for films of face-centered-cubic lattice. Our results show that in the limit of L\ensuremath{\rightarrow}\ensuremath{\infty}, ${\mathit{T}}_{\mathit{c}}$ approaches the corresponding bulk value rather quickly with increasing m in both cases.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsMar 1, 199412 citations

Study of critical phenomena of quantum spin systems by spin-cluster approximation series

Hiroshi Mano

WORLD SCIENTIFIC eBooksSep 1, 19950 citations

{\mathit{T}}_{\mathit{c}}

(l) for (d+1)-dimensional Ising films to any order cumulant as a function of the number l of hyperlayers in the hyperfilm. Explicit expressions up to the fourth order are given. It is shown from the general expression for

{\mathit{T}}_{\mathit{c}}^{(\mathit{m})}

(l) that [

{\mathit{T}}_{\mathit{c}}

(l)-

{\mathit{T}}_{\mathit{c}}

{\mathit{T}}_{\mathit{c}}

=b/(l+a) in the limit l\ensuremath{\rightarrow}\ensuremath{\infty}. Comparisons with existing results for d=2 are discussed.

Following the approach recently proposed by Lin, Che, and Xia [Phys. Rev. A 46, 1805 (1992)], we calculate the critical temperature

{\mathit{T}}_{\mathit{c}}

for Ising films with lattice structures other than simple cubic by means of the variational cumulant expansion (VCE) of the free energy of the spin system. The critical temperature is derived in terms of the ratio of two successive cumulants to an arbitrary order of accuracy. Since the cumulant of any order m can be calculated analytically by a graphic method, analytical expressions of

{\mathit{T}}_{\mathit{c}}

can be derived, in principle, as functions of the number L of spin layers in the film to an arbitrary order of accuracy in the VCE. We describe the graphic method in great detail in this paper, and calculate

{\mathit{T}}_{\mathit{c}}

up to the fourth-order cumulant for films of body-centered-cubic lattice and to the third order for films of face-centered-cubic lattice. Our results show that in the limit of L\ensuremath{\rightarrow}\ensuremath{\infty},

{\mathit{T}}_{\mathit{c}}

approaches the corresponding bulk value rather quickly with increasing m in both cases.