Abstract
The susceptibility of the Ising model on a kagomé lattice has never been obtained. We investigate the properties of the kagomé-lattice Ising model by using the Wang-Landau sampling method. We estimate both the magnetic scaling exponent yh = 1.90(1) and the thermal scaling exponent yt = 1.04(2) only from the susceptibility. From the estimated values of yh and yt, we obtain all the critical exponents, the specific-heat critical exponent α = 0.08(4), the spontaneous-magnetization critical exponent β = 0.10(1), the susceptibility critical exponent γ = 1.73(5), the isothermalmagnetization critical exponent δ = 16(4), the correlation-length critical exponent ν = 0.96(2), and the correlation-function critical exponent η = 0.20(4), without using any other thermodynamic function, such as the specific heat, magnetization, correlation length, and correlation function. One should note that the evaluation of all the critical exponents only from information on the susceptibility is an innovative approach.
Similar content being viewed by others
References
I. Syozi, Prog. Theo. Phys. 6, 306 (1951).
M. Mekata, Physics Today 56, 12 (2003). and references therein.
V. Elser, Phys. Rev. Lett. 62, 2405 (1989).
J. L. Atwood, Nature Mater. 1, 91 (2002). and references therein.
Q. Chen, S. C. Bae and S. Granick, Nature 469, 306 (2011).
K. S. Khalil, A. Sagastegui, Y. Li, M. A. Tahir, J. E. S. Socolar, B. J. Wiley and B. B. Yellen, Nature Commun. 3, 794 (2012).
Y. Zong et al., Optics Express 24, 8877 (2016). and references therein.
I. Syozi, Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic Press, New York, 1972), Vol. 1, p. 269.
K. Kano and S. Naya, Prog. Theor. Phys. 10, 158 (1953).
S. Naya, Prog. Theor. Phys. 11, 53 (1954).
A. J. Guttmann, J. Phys. A 10, 1911 (1977).
H. Giacomini, J. Phys. A 21, L31 (1988).
K. Y. Lin, J. Phys. A 22, 3435 (1989).
L. Onsager, Phys. Rev. 65, 117 (1944).
C. Domb, The Critical Point (Taylor and Francis, London, 1996), and references therein.
J. Cardy, Finite-Size Scaling (North-Holland, Amsterdam, 1988), Vol. 1.
G. M. Torrie and J. P. Valleau, J. Comput. Phys. 23, 187 (1977).
E. Marinari and G. Parisi, Europhys. Lett. 19, 451 (1992).
W. Kwak and U. H. E. Hansman, Phys. Rev. Lett. 95, 138102 (2005).
B. A. Berg and T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992).
B. A. Berg, Int. J. Mod. Phys. C 4, 249 (1993).
F. Eisenmenger, U. H. E. Hansmann, Sh. Hayryan and C. K. Hu, Comp. Phys. Comm. 138, 192 (2001).
F. Eisenmenger, U. H. E. Hansmann, S. Hayryan and C-K. Hu, Comp. Phys. Comm. 174, 422 (2006).
David P. Landau, Monte-Carlo Simulations in Statistical Physics, 3rd ed. (Cambridge, New York, 2009)
F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001).
D. P. Landau, S-H. Tsai and M. Exler, Am. J. Phys. 72, 1294 (2004).
B. J. Schulz, K. Binder, M. Müller and D. P. Landau, Phys. Rev. E 67, 067102 (2003).
M. Scott Shell, P. G. Debenedetti and A. Z. Panagiotopoulos, Phys. Rev. E 66, 056703 (2002).
C. Zhou, T. C. Schulthess, S. Torbrügge and D. P. Landau, Phys. Rev. Lett. 96, 120201 (2006).
C. Yamaguchi and Y. Okabe, J. Phys. A: Math. Gen. 34, 8781 (2001).
F. Wang and D. P. Landau, Phys. Rev. E 64, 056101 (2001).
T. S. Jain and J. J. de Pablo, J. Chem. Phys. 118, 4226 (2003).
Q. L. Yan, R. Faller and J. J. de Pablo, J. Chem. Phys. 116, 8745 (2002).
N. Rathore, T. A. Knotts and J. J. de Pablo, J. Chem. Phys 118, 4285 (2003).
J-S. Yang and W. Kwak, Comput. Phys. Comm. 179, 179 (2008).
F. Calvo, Mol. Phys. 100, 3421 (2002).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, SY., Kwak, W. Susceptibility of the Ising Model on a Kagomé Lattice by Using Wang-Landau Sampling. J. Korean Phys. Soc. 72, 653–657 (2018). https://doi.org/10.3938/jkps.72.653
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3938/jkps.72.653