Regensburg 2007 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 15: Internal Symposium: Finite size effects at phase transitions
DY 15.4: Invited Talk
Tuesday, March 27, 2007, 15:45–16:15, H2
Diversity of critical behavior within a universality class — •Volker Dohm — RWTH Aachen
The notion of a universality class of critical phenomena in bulk and confined systems is discussed. The Privman-Fisher hypothesis [1] states that, for given geometry and boundary conditions, finite-size scaling functions are universal, i.e., independent of microscopic details, and that two-scale factor universality is valid for confined systems. In recent years it has been shown that renormalization-group (RG) theory is well compatible with a certain degree of diversity of finite-size critical behavior within a universality class. There are at least two microscopic sources of nonuniversal effects near criticality : (i) van der Waals type interactions in fluids and (ii) anisotropic interactions in solids. While critical exponents are not affected by these sources, a nontrivial dependence of finite-size scaling functions on these sources has been predicted [2, 3]. New RG results of the anisotropic ϕ4 theory are presented that illustrate the nonuniversality of finite-size critical behavior. Recent MC simulations [4] for anisotropic Ising models support this diversity.
- [1] V. Privman and M.E. Fisher, Phys. Rev. B 30, 322 (1984).
- [2] X.S. Chen and V. Dohm, Phys. Rev. E 70, 056136 (2004); Physica B 329-333, 202 (2003).
- [3] V. Dohm, J. Phys. A 39, L 259 (2006).
- [4] M. Schulte and C. Drope, Int. J. Mod. Phys. C 16, 1217 (2005); W. Selke and L.N. Shchur, J. Phys. A 38, L 739 (2005).