Critical phenomena in films of finite thickness are considered. A detailed scaling theory, with allowance for distinct exponents $\ensuremath{\lambda}$ and $\ensuremath{\theta}=\frac{1}{\ensuremath{\nu}}$ for the critical-point shift and rounding, respectively, is confirmed by exact calculations on $d$ -dimensional ferromagnetic spherical models and ideal Bose fluids with various boundary conditions. Isingmodel results and existing data on real helium films are consistent with the theory.Critical phenomena in films of finite thickness are considered. A detailed scaling theory, with allowance for distinct exponents $\ensuremath{\lambda}$ and $\ensuremath{\theta}=\frac{1}{\ensuremath{\nu}}$ for the critical-point shift and rounding, respectively, is confirmed by exact calculations on $d$-dimensional ferromagnetic spherical models and ideal Bose fluids with various boundary conditions. Isingmodel results and existing data on real helium films are consistent with the theory.

Physical Review LettersJun 5, 19721,518 citations

Theory of Critical Phenomena in Finite-Size Systems

J.G. Brankov, Daniel M. Danchev, N. S. Tonchev

Series in modern condensed matter physicsAug 1, 2000203 citations

Nonlinear critical dynamics of a spherical model

Zoltàn Ràcz, Tamás Tél

Physics Letters AJan 1, 197717 citations

Finite–size effects in the spherical model of finite thickness

Hassan Chamati, Universität Duisburg–essen Fachbereich Physik

A detailed analysis of the finite–size effects on the bulk critical behaviour of the d–dimensional mean spherical model confined to a film geometry with finite thickness L is reported. Along the finite direction different boundary conditions are applied: periodic (p), antiperiodic (a) and free surfaces with Dirichlet (D), Neumann (N) and a combination of Neumann and Dirichlet (ND) on both surfaces. A systematic method for the evaluation of the finite–size corrections to the free energy for the different types of boundary conditions is proposed. The free energy density and the equation for the spherical field are computed for arbitrary d. It is found, for 2 < d < 4, that the singular part of the free energy has the required finite–size scaling form at the bulk critical temperature only for (p) and (a). For the remaining boundary conditions the standard finite–size scaling hypothesis is not valid. At d = 3, the critical amplitude (related to the so called Casimir amplitude) is estimated. We obtainA detailed analysis of the finite–size effects on the bulk critical behaviour of the d–dimensional mean spherical model confined to a film geometry with finite thickness L is reported. Along the finite direction different boundary conditions are applied: periodic (p), antiperiodic (a) and free surfaces with Dirichlet (D), Neumann (N) and a combination of Neumann and Dirichlet (ND) on both surfaces. A systematic method for the evaluation of the finite–size corrections to the free energy for the different types of boundary conditions is proposed. The free energy density and the equation for the spherical field are computed for arbitrary d. It is found, for 2 < d < 4, that the singular part of the free energy has the required finite–size scaling form at the bulk critical temperature only for (p) and (a). For the remaining boundary conditions the standard finite–size scaling hypothesis is not valid. At d = 3, the critical amplitude (related to the so called Casimir amplitude) is estimated. We obtain

Aug 4, 20134 citations

Finite-size effects in the spherical model of finite thickness

H Chamati

A detailed analysis of the finite-size effects on the bulk critical behaviour of the d -dimensional mean spherical model confined to a film geometry with finite thickness L is reported. Along the finite direction different kinds of boundary conditions are applied: periodic ( p ), antiperiodic ( a ) and free surfaces with Dirichlet ( D ), Neumann ( N ) and a combination of Neumann and Dirichlet ( ND ) on both surfaces. A systematic method for the evaluation of the finite-size corrections to the free energy for the different types of boundary conditions is proposed. The free energy density and the equation for the spherical field are computed for arbitrary d . It is found, for 2 < d < 4, that the singular part of the free energy has the required finite-size scaling form at the bulk critical temperature only for ( p ) and ( a ). For the remaining boundary conditions the standard finite-size scaling hypothesis is not valid. At d = 3, the critical amplitude of the singular part of the free energy (related to the so-called Casimir amplitude) is estimated. We obtain Δ ( p ) = −2ζ(3)/(5π) = −0.153 051..., Δ ( a ) = 0.274 543... and Δ ( ND ) = 0.019 22..., implying a fluctuation-induced attraction between the surfaces for ( p ) and repulsion in the other two cases. For ( D ) and ( N ) we find a logarithmic dependence on L .A detailed analysis of the finite-size effects on the bulk critical behaviour of the d -dimensional mean spherical model confined to a film geometry with finite thickness L is reported. Along the finite direction different kinds of boundary conditions are applied: periodic ( p ), antiperiodic ( a ) and free surfaces with Dirichlet ( D ), Neumann ( N ) and a combination of Neumann and Dirichlet ( ND ) on both surfaces. A systematic method for the evaluation of the finite-size corrections to the free energy for the different types of boundary conditions is proposed. The free energy density and the equation for the spherical field are computed for arbitrary d . It is found, for 2 < d < 4, that the singular part of the free energy has the required finite-size scaling form at the bulk critical temperature only for ( p ) and ( a ). For the remaining boundary conditions the standard finite-size scaling hypothesis is not valid. At d = 3, the critical amplitude of the singular part of the free energy (related to the so-called Casimir amplitude) is estimated. We obtain Δ ( p ) = −2ζ(3)/(5π) = −0.153 051..., Δ ( a ) = 0.274 543... and Δ ( ND ) = 0.019 22..., implying a fluctuation-induced attraction between the surfaces for ( p ) and repulsion in the other two cases. For ( D ) and ( N ) we find a logarithmic dependence on L .

arXiv:0805.0715Journal of Physics A Mathematical and TheoreticalAug 11, 200813 citations

d

-dimensional ferromagnetic spherical models and ideal Bose fluids with various boundary conditions. Isingmodel results and existing data on real helium films are consistent with the theory.