Exact results of the finite-size behaviour of the susceptibility in three-dimensional mean spherical model films under Dirichlet–Dirichlet, Dirichlet–Neumann and Neumann–Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature T c are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent λ characterizing the shift of the finite-size critical temperature with respect to T c is smaller than 1/ν, with ν being the critical exponent of the bulk correlation length.Exact results of the finite-size behaviour of the susceptibility in three-dimensional mean spherical model films under Dirichlet–Dirichlet, Dirichlet–Neumann and Neumann–Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature T c are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent λ characterizing the shift of the finite-size critical temperature with respect to T c is smaller than 1/ν, with ν being the critical exponent of the bulk correlation length.

arXiv:cond-mat/0305470Journal of Physics A Mathematical and GeneralAug 12, 20035 citations

Violation of finite-size scaling in the spherical limit of the ϕ4 theory

X Chen

Physica B Condensed MatterJul 1, 20002 citations

Low-temperature regimes and finite-size scaling in a quantum spherical model

Hassan Chamati, Daniel M. Danchev, Ekaterina S. Pisanova +1 more

A $d$ --dimensional quantum model in the spherical approximation confined to a general geometry of the form $L^{d-d^{\prime}} \times\infty^{d^{\prime}}\times L_τ^{z}$ ( $L$ --linear space size and $L_τ$ --temporal size) and subjected to periodic boundary conditions is considered. Because of its close relation with the quantum rotors model it can be regarded as an effective model for studying the low-temperature behavior of the quantum Heisenberg antiferromagnets. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions $1A $d$--dimensional quantum model in the spherical approximation confined to a general geometry of the form $L^{d-d^{\prime}} \times\infty^{d^{\prime}}\times L_τ^{z}$ ($L$--linear space size and $L_τ$--temporal size) and subjected to periodic boundary conditions is considered. Because of its close relation with the quantum rotors model it can be regarded as an effective model for studying the low-temperature behavior of the quantum Heisenberg antiferromagnets. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions $1

arXiv:cond-mat/9707280Jul 28, 19973 citations

Theory of a spherical-quantum-rotors model: Low-temperature regime and finite-size scaling

Hassan Chamati, Ekaterina S. Pisanova, N. S. Tonchev

The quantum-rotors model can be regarded as an effective model for the low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we consider a $d$ -dimensional model in the spherical approximation confined to a general geometry of the form ${L}^{d\ensuremath{-}{d}^{\ensuremath{'}}}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\infty}}^{{d}^{\ensuremath{'}}}\ifmmode\times\else\texttimes\fi{}{L}_{\ensuremath{\tau}}^{z}$ $(L$ -linear space size and ${L}_{\ensuremath{\tau}}$-temporal size) and subjected to periodic boundary conditions. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions $1<d<3$ and $0<~{d}^{\ensuremath{'}}<~d$ a detailed analysis, in terms of the special functions of classical mathematics, for the susceptibility and the equation of state is given. Particular attention is paid to the two-dimensional case.The quantum-rotors model can be regarded as an effective model for the low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we consider a $d$-dimensional model in the spherical approximation confined to a general geometry of the form ${L}^{d\ensuremath{-}{d}^{\ensuremath{'}}}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\infty}}^{{d}^{\ensuremath{'}}}\ifmmode\times\else\texttimes\fi{}{L}_{\ensuremath{\tau}}^{z}$ $(L$-linear space size and ${L}_{\ensuremath{\tau}}$-temporal size) and subjected to periodic boundary conditions. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions $1<d<3$ and $0<~{d}^{\ensuremath{'}}<~d$ a detailed analysis, in terms of the special functions of classical mathematics, for the susceptibility and the equation of state is given. Particular attention is paid to the two-dimensional case.

arXiv:cond-mat/9701159Physical review. B, Condensed matterMar 1, 199829 citations

Nonlinear critical dynamics of a spherical model

Zoltàn Ràcz, Tamás Tél

Physics Letters AJan 1, 197717 citations

d

--dimensional quantum model in the spherical approximation confined to a general geometry of the form

L^{d-d^{\prime}} \times\infty^{d^{\prime}}\times L_τ^{z}

(

L

--linear space size and

L_τ

--temporal size) and subjected to periodic boundary conditions is considered. Because of its close relation with the quantum rotors model it can be regarded as an effective model for studying the low-temperature behavior of the quantum Heisenberg antiferromagnets. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions $1

The quantum-rotors model can be regarded as an effective model for the low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we consider a

d

-dimensional model in the spherical approximation confined to a general geometry of the form ${L}^{d\ensuremath{-}{d}^{\ensuremath{'}}}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\infty}}^{{d}^{\ensuremath{'}}}\ifmmode\times\else\texttimes\fi{}{L}_{\ensuremath{\tau}}^{z}$

(L

-linear space size and ${L}_{\ensuremath{\tau}}$-temporal size) and subjected to periodic boundary conditions. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions

1<d<3

and $0<~{d}^{\ensuremath{'}}<~d$ a detailed analysis, in terms of the special functions of classical mathematics, for the susceptibility and the equation of state is given. Particular attention is paid to the two-dimensional case.