https://doi.org/10.1140/epjb/e2020-10422-9
Regular Article
Why boundary conditions do not generally determine the universality class for boundary critical behavior
Fakultät für Physik, Universität Duisburg-Essen,
D-47058
Duisburg, Germany
a e-mail: h.w.diehl@uni-due.de
Received:
17
August
2020
Received in final form:
30
August
2020
Accepted:
4
September
2020
Published online: 12 October 2020
Interacting field theories for systems with a free surface frequently exhibit distinct universality classes of boundary critical behaviors depending on gross surface properties. The boundary condition satisfied by the continuum field theory on some scale may or may not be decisive for the universality class that applies. In many recent papers on boundary field theories, it is taken for granted that Dirichlet or Neumann boundary conditions decide whether the ordinary or special boundary universality class is observed. While true in a certain sense for the Dirichlet boundary condition, this is not the case for the Neumann boundary condition. Building on results that have been worked out in the 1980s, but have not always been appropriately appreciated in the literature, the subtle role of boundary conditions and their scale dependence is elucidated and the question of whether or not they determine the observed boundary universality class is discussed.
Key words: Statistical and Nonlinear Physics
© The Author(s) 2020. This article is published with open access at Springerlink.com
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Open Access funding enabled and organized by Projekt DEAL.
