Thermodynamic Casimir effects involving interacting field theories with zero modes
Thermodynamic Casimir effects involving interacting field theories with zero modes
复制标题
涉及零模式相互作用场论的热力学卡西米尔效应
DOI：
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
H. Diehl
中科院分区：
文献类型：
--
作者：
D. Gruneberg;H. Diehl
Systems with an O(n) symmetrical Hamiltonian are considered in a d-dimensional slab geometry of macroscopic lateral extension and finite thickness L that undergo a continuous bulk phase transition in the limit L{yields}{infinity}. The effective forces induced by thermal fluctuations at and above the bulk critical temperature T{sub c,{infinity}} (thermodynamic Casimir effect) are investigated below the upper critical dimension d*=4 by means of field-theoretic renormalization-group methods for the case of periodic and special-special boundary conditions, where the latter correspond to the critical enhancement of the surface interactions on both boundary planes. As shown previously [Europhys. Lett. 75, 241 (2006)], the zero modes that are present in Landau theory at T{sub c,{infinity}} make conventional renormalization-group-improved perturbation theory in 4-{epsilon} dimensions ill-defined. The revised expansion introduced there is utilized to compute the scaling functions of the excess free energy and the Casimir force for temperatures T{>=}T{sub c,{infinity}} as functions of L{identical_to}L/{xi}{sub {infinity}}, where {xi}{sub {infinity}} is the bulk correlation length. Scaling functions of the L-dependent residual free energy per area are obtained, whose L{yields}0 limits are in conformity with previous results for the Casimir amplitudes {delta}{sub C} to O({epsilon}{sup 3/2}) and display a more reasonable small-L behavior inasmuch as they approach the criticalmore » value {delta}{sub C} monotonically as L{yields}0. Extrapolations to d=3 for the Ising case n=1 with periodic boundary conditions are in fair agreement with Monte Carlo results. In the case of special-special boundary conditions, extrapolations to d=3 are hampered by the fact that the one-loop result for the inverse finite-size susceptibility becomes negative for some values of L when {epsilon} > or approx. 0.83.« less
Systems with an O(n) symmetrical Hamiltonian are considered in a d-dimensional slab geometry of macroscopic lateral extension and finite thickness L that undergo a continuous bulk phase transition in the limit L{yields}{infinity}. The effective forces induced by thermal fluctuations at and above the bulk critical temperature T{sub c,{infinity}} (thermodynamic Casimir effect) are investigated below the upper critical dimension d*=4 by means of field-theoretic renormalization-group methods for the case of periodic and special-special boundary conditions, where the latter correspond to the critical enhancement of the surface interactions on both boundary planes. As shown previously [Europhys. Lett. 75, 241 (2006)], the zero modes that are present in Landau theory at T{sub c,{infinity}} make conventional renormalization-group-improved perturbation theory in 4-{epsilon} dimensions ill-defined. The revised expansion introduced there is utilized to compute the scaling functions of the excess free energy and the Casimir force for temperatures T{>=}T{sub c,{infinity}} as functions of L{identical_to}L/{xi}{sub {infinity}}, where {xi}{sub {infinity}} is the bulk correlation length. Scaling functions of the L-dependent residual free energy per area are obtained, whose L{yields}0 limits are in conformity with previous results for the Casimir amplitudes {delta}{sub C} to O({epsilon}{sup 3/2}) and display a more reasonable small-L behavior inasmuch as they approach the criticalmore » value {delta}{sub C} monotonically as L{yields}0. Extrapolations to d=3 for the Ising case n=1 with periodic boundary conditions are in fair agreement with Monte Carlo results. In the case of special-special boundary conditions, extrapolations to d=3 are hampered by the fact that the one-loop result for the inverse finite-size susceptibility becomes negative for some values of L when {epsilon} > or approx. 0.83.« less