Abstract
The exact specific heats of the Ising ferromagnet on L × L square lattices (L = 3 ~ 16) with self-dual boundary conditions are evaluated using the microcanonical transfer matrix and high-performance massive computing. From the specific heats, we obtain the shift exponent λ = 1.879(9) for the square-lattice Ising ferromagnet with self-dual boundary conditions in the thermodynamic limit (L → ∞) for the first time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Domb, The Critical Point (Taylor and Francis, London, 1996).
A. E. Ferdinand and M. E. Fisher, Phys. Rev. 185, 832 (1969).
M. N. Barber, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, New York, 1983), Vol. 8, p. 145.
C. Hoelbling and C. B. Lang, Phys. Rev. B 54, 3434 (1996).
W. Janke and R. Kenna, Phys. Rev. B 65, 064110 (2002).
S.-Y. Kim, J. Korean Phys. Soc. 59, 2980 (2011).
S.-Y. Kim and R. J. Creswick, Phys. Rev. Lett. 81, 2000 (1998).
S.-Y. Kim and R. J. Creswick, Phys. Rev. E 63, 066107 (2001).
S.-Y. Kim, Phys. Rev. E 70, 016110 (2004).
S.-Y. Kim, Phys. Rev. Lett. 93, 130604 (2004).
F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).
R. Bulirsch and J. Stoer, Numer. Math. 6, 413 (1964).
W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in Fortran 77, 2nd edition (Cambridge University Press, Cambridge, 1992), p. 104.
J. H. Lee, S.-Y. Kim and J. Lee, J. Chem. Phys. 133, 114106 (2010); J. Chem. Phys. 135, 204102 (2011); Phys. Rev. E 86, 011802 (2012); Phys. Rev. E 87, 052601 (2013).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, SY. Study on the square-lattice Ising model with self-dual boundary conditions. Journal of the Korean Physical Society 65, 2009–2012 (2014). https://doi.org/10.3938/jkps.65.2009
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3938/jkps.65.2009