Abstract
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.
Graphical abstract
Article PDF
Similar content being viewed by others
References
T.C. Lubensky, M.H. Rubin, Phys. Rev. B 11, 4533 (1975)
T.C. Lubensky, M.H. Rubin, Phys. Rev. B 12, 3885 (1975)
A.J. Bray, M.A. Moore, J. Phys. A: Math. Gen. 10, 1927 (1977)
K. Binder, inPhase transitions and critical phenomena, edited by C. Domb, J.L. Lebowitz (Academic, London, 1983), Vol. 8, pp. 1–144
H.W. Diehl, inPhase transitions and critical phenomena, edited by C. Domb, J.L. Lebowitz (Academic, London, 1986), Vol. 10, pp. 75–267
H.W. Diehl, Int. J. Mod. Phys. B 11, 3503 (1997)
H.W. Diehl, J. Appl. Phys. 53, 7914 (1982)
J.S. Reeve, A.J. Guttmann, Phys. Rev. Lett. 45, 1581 (1980)
H.W. Diehl, S. Dietrich, Phys. Lett. A 80, 408 (1980)
J.S. Reeve, Phys. Lett. A 81, 237 (1981)
H.W. Diehl, S. Dietrich, Z. Phys. B 42, 65 (1981)
H.W. Diehl, S. Dietrich, Phys. Rev. B 24, 2878 (1981)
H.W. Diehl, S. Dietrich, Z. Phys B 50, 117 (1983)
H.W. Diehl, A. Nüsser, Phys. Rev. Lett. 56, 2834 (1986)
A.J. Bray, M.A. Moore, Phys. Rev. Lett. 38, 735 (1977)
K. Ohno, Y. Okabe, Phys. Lett. A 99, 54 (1983)
K. Ohno, Y. Okabe, Progr. Theor. Phys. 70, 1226 (1983)
K. Ohno, Y. Okabe, Progr. Theor. Phys. 72, 736 (1984)
H.W. Diehl, M. Shpot, Phys. Rev. Lett. 73, 3431 (1994)
H.W. Diehl, M. Shpot, Nucl. Phys. B 528, 595 (1998)
D.P. Landau, K. Binder, Phys. Rev. B 41, 4633 (1990)
C. Ruge, S. Dunkelmann, F. Wagner, J. Wulf, J. Stat. Phys. 73, 293 (1993)
M. Pleimling, W. Selke, Eur. Phys. J. B 1, 385 (1998)
M. Krech, Phys. Rev. B 62, 6360 (2000)
M. Pleimling, J. Phys. A: Math. Gen. 37, R79 (2004)
Y. Deng, H.W.J. Blöte, M.P. Nightingale, Phys. Rev. E 72, 016128 (2005)
M. Hasenbusch, Phys. Rev. B 84, 134405 (2011)
M. Hasenbusch, Phys. Rev. B 83, 134425 (2011)
A. Belavin, A. Polyakov, A. Zamolodchikov, Nucl. Phys. B 241, 333 (1984)
A.A. Belavin, A.M. Polyakov, A.B. Zamolodchikov, J. Stat. Phys. 34, 763 (1984)
J.L. Cardy, Nucl. Phys. B 240, 514 (1984)
P.D. Francesco, P. Mathieu, D. Senechal,Conformal field theory (Springer, Berlin, 1997)
P. Ginsparg, inFields, strings and critical phenomena, edited by E. Brézin, J. Zinn-Justin (North-, Amsterdam, 1990), pp. 3–168
D. Poland, S. Rychkov, A. Vichi, Rev. Mod. Phys. 91, 015002 (2019)
P. Liendo, L. Rastelli, B.C. Rees, J. High Energy Phys. 2013, 1 (2013)
F. Gliozzi, P. Liendo, M. Meineri, A. Rago, J. High Energy Phys. 2015, 36 (2015)
A. Bissi, T. Hansen, A. Söderberg, J. High Energy Phys. 2019, 10 (2019)
A. Kaviraj, M.F. Paulos, J. High Energy Phys. 2020, 135 (2020)
C.P. Herzog, K.W. Huang, J. High Energy Phys. 2017, 189 (2017)
C.P. Herzog, I. Shamir, J. High Energy Phys. 2019, 88 (2019)
M.A. Shpot, arXiv:1912.03021 (2019)
C.P. Herzog, N. Kobayashi, J. High Energy Phys. 2020, 126 (2020)
V. Procházka, A. Söderberg, J. High Energy Phys. 2020, 114 (2020)
P. Dey, T. Hansen, M. Shpot, arXiv:2006.11253 (2020)
M. Lüscher, J. High Energy Phys. 2006, 042 (2006)
K.G. Wilson, J. Kogut, Phys. Rep. 12, 75 (1974)
D. Grüneberg, H.W. Diehl, Phys. Rev. B 77, 115409 (2008)
H.W. Diehl, F.M. Schmidt, New J. Phys. 13, 123025 (2011)
K. Symanzik, Lett. Nuovo Cimento 8, 771 (1973)
R.B. Griffiths, J. Math. Phys. 8, 478 (1967)
D.G. Kelly, S. Sherman, J. Math. Phys. 9, 466 (1968)
H.W. Diehl, M. Smock, Phys. Rev. B 47, 5841 (1993) [Erratum: Ibid. 48, 6740 (1993)]
M. Krech, S. Dietrich, Phys. Rev. Lett. 66, 345 (1991) [Erratum: Ibid. 67, 1055 (1991)]
M. Krech, S. Dietrich, Phys. Rev. A 46, 1886 (1992)
M. Krech,Casimir effect in critical systems (World Scientific, Singapore, 1994)
F.M. Schmidt, H.W. Diehl, Phys. Rev. Lett. 101, 100601 (2008)
Acknowledgments
Open Access funding enabled and organized by Projekt DEAL.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access 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.
About this article
Cite this article
Diehl, H.W. Why boundary conditions do not generally determine the universality class for boundary critical behavior. Eur. Phys. J. B 93, 195 (2020). https://doi.org/10.1140/epjb/e2020-10422-9
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjb/e2020-10422-9