Investigation Of Critical Casimir Effects With Field Theoretic Method

The Casimir effect is a phenomenon common to all systems with fluctuations which are confined by some boundaries. In nature fluctuations and boundaries are ubiquitous, so the Casimir effect plays an important role in the different fields of sciences such as atomic and molecular physics,condensed matter physics,quantum field theory,chemistry,biology, astrophysics,cosmology and et al.The Casimir effect was first proposed by H.B.G.Casimir in 1948. He has calculated the Casimir force induced by quantum fluctuations confined between two uncharged conducting plates. Great progresses have been made for the quantum Casimir effects recently because of the experimental confirmation . In 1978 M.E. Fisher and P.G. de Gennes proposed critical Casimir effect induced by the fluctuations of order-parameter in critical phenomena. The studies of the critical Casimir effects become very active just recently.The critical Casimir effects of two-dimension Ising stripe and spherical model can be calculated exactly, but their results cannot be compared with experimental data. The Ginzburg-Landau-Wilson(GLW) model can be used to describe real systems, but it can be calculated only perturbatively. Until now no perturbation approach has been found which can be used in the whole critical range of infinite film systems and the theoretical predictions of critical Casimir effect are restricted at ancl above critical point. The results of the analytic results and experiment data indicates that the Casimir forces is much stronger below the critical point.Using the field theory and renormalization group theory, we have studied the Casimir effect of a infinite film system in the whole critical range. We employ the minimal renormalization scheme at fixed d < 4 dimension without using the e = 4 -dexpansion and dimensional regularization method. For periodic boundary condition, we have calculated the Casimir free energy density and pressurescaling functions in one-loop order approximation. Above critical point our result is identical to the dimensional regularization result. In the whole critical region our results agree qualitatively with the recent Monte-Carlo simulation. For Dirichlet-Dirichlet boundary conditions we have got the results in a mean-field approximative(MFA). Although MFA is a very rough approximation, the theoretic predictions of Casimir pressure scaling function have the qualitative features of the experimental data.