Critical behavior of interacting surfaces with tension

Abstract

Dedicated to Johannes Zittartz on the occasion of his 60th birthday.Abstract. Wetting phenomena, molecular protrusions of lipid bilayers and membrane stacks under lateral tension provide physical examples for interacting surfaces with tension. Such surfaces are studied theoretically using functional renormalization and Monte Carlo simulations. The critical behavior arising from thermally-excited shape fluctuations is determined both for global quantities such as the mean separation of these surfaces and for local quantities such as the probabilities for local contacts.PACS. 64.60.-i General studies of phase transitions -68.35.Ct Interface structure and roughness

Van der Waals interaction between flux lines in high- superconductors: A variational approach

“…(14) Next, the expectation value H − H 0 0 shall be calculated. To proceed, it is useful to rewrite the last term in the interaction part of (5) using the Fourier representation (7). Then, the averaging can be immediately carried out, leading to…”

“…x ≥ x 2 (23) with x 1 = 1 and x 2 = 5. The choice of the cutoff function, as well as the actual values of x 1 and x 2 , is to some extent arbitrary; x 1 = 1 is however an obvious choice, and x 2 has to be chosen such that the cutoff is not too sharp and, on the other hand, does not influence the form of the potential in the vicinity of the minimum for those values of a vdw that are physically meaningful [7].…”

“…In order to make quantitative predictions for the lowfield phase diagram of layered high-T c superconductors, we identify the parameters introduced above with physical parameters characterizing those systems: The elastic constant isκ = ε • /2k B T in the long wavelength regime λk z ≪ 1 [8], and the amplitude of the vdW attraction (relative to v 0 ) is given by a vdw ≈ k B T /(2ε • d ln 2 (πλ/d)), where d is the layer spacing [4,7].…”

“…Here, ε 2 = m/M ≪ 1 denotes the anisotropy of the material with m and M the effective masses parallel and perpendicular to the CuO 2 plane, respectively, and d the interlayer spacing. Apart from this thermally induced attraction, also frozen-in disorder in impure superconductors induces an attraction between flux lines with the same dependence on the distance R [6,7]. This disorder induced attraction dominates at very low temperature T ≪ T dis , where T dis depends on the disorder strength [3].…”

“…This scaling approach is elegant and simple and yields the correct qualitative picture, but does not allow for quantitative predictions. More recently a functional renormalization group (RG) calculation has been adapted to the same problem [7]; in particular, the low field phase diagram of Bi 2 Sr 2 CaCu 2 O x (BiSCCO) was calculated. In that approach, the bare flux line interaction is renormalized by thermal fluctuations on all scales between λ and a, providing an effective free energy on the scale of a.…”