Finite size critical behavior for Dirichlet boundary conditions

Holographic Video System using Fourier Transform and Data Reduction

“…In section 4 we calculate 5 at the bulk critical temperature T, and find a radically different scaling behaviour depending on whether I+j >O or IT^ =O; the observed difference is even more striking when d is close to, or greater than, 4. Under 'twisted' boundary conditions the correlation length follows closely the behaviour found in d = 4 -E dimensions under free (Dirichlet) boundary conditions (Eisenriegler 1985) or in the king model with d > 4 again under free boundary conditions (Rudnick et a1 1985), and bears little resemblance to the results pertaining to the periodic case. In section 5 we close the paper with some general remarks on the problem studied here.…”

“…However, only limited results are available for systems under non-periodic boundary conditions, such as Eisenriegler (1985), Henkel (1988), Henkel and Weston (1992). Here we provide results for the correlation length c(T,; L) of the spherical model under 'twisted' boundary conditions in general geometry Ld-& x cod' for several regimes of d.…”

Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions

“…On the other hand, universal amplitude ratios have been found for critical systems contained in parallel plates with nonperiodic boundary conditions [22]. Furthermore, field-theoretic renormalization-group calculations have apparently confirmed the validity of universal finite-size scaling within the ϕ 4 field theory with Dirichlet boundary conditions: Universal finite-size amplitude ratios [23] and universal finite-size contributions to the free energy density and to the critical Casimir force were calculated both in the Gaussian (one-loop) approximation [24,25,26] as well as in two-loop order [25].…”

“…All calculations, however, were carried out within the dimensional regularization scheme which neglects cutoff effects. As pointed out by Dohm [9,35], an unresolved feature of the dimensionally regularized perturbative results for U surf ace [23,25,35,41,42] is a pole term ∼ (d − 3) −1 that diverges in three dimensions.…”

“…Related field-theoretic predictions have also been presented for surface quantities [28,29]. In these papers [23,24,25,26,27,28,29], however, the method of dimensional regularization was employed which neglects lattice and cutoff effects.…”