Abstract
The critical behavior of the disordered two-dimensional antiferromagnetic Potts model with the number of spin states q= 3 on a triangular lattice with disorder in the form of nonmagnetic impurities is studied by the Monte Carlo method. The critical exponents for the susceptibility γ, magnetization β, specific heat α, and correlation radius ν are calculated in the framework of the finite-size scaling theory at spin concentrations p = 0.90, 0.80, 0.70, and 0.65. It is found that the critical exponents increase with the degree of disorder, whereas the ratios and do not change, thus holding the scaling equality \(\frac{{2\beta }}{\nu } + \frac{\gamma }{\nu } = d\). Such behavior of the critical exponents is related to the weak universality of the critical behavior characteristic of disordered systems. All results are obtained using independent Monte Carlo algorithms, such as the Metropolis and Wolff algorithms.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. S. Dotsenko, Phys. Usp. 38, 457 (1995).
R. Fol’k, Yu. Golovach, and T. Yavorskii, Phys. Usp. 46, 169 (2003).
A. K. Murtazaev, Phys. Usp. 49, 1092 (2006).
A. B. Harris, J. Phys.. 7, 1671 (1974).
Vik. Dotsenko and Vl. Dotsenko, Adv. Phys. 32, 129 (1983).
Y. Imry and M. Wortis, Phys. Rev.. 19, 3580 (1979).
M. Aizenman and J. Wehr, Phys. Rev. Lett. 62, 2503 (1989).
C. R. Vasquez, R. V. Paredes, A. Hasmy, and R. Jullien, Phys. Rev. Lett. 90, 170602 (2003).
K. Hui and A. N. Berker, Phys. Rev. Lett. 62, 2507 (1989).
J. Q. Yin, B. Zheng, V. V. Prudnikov, and S. Trimper, Eur. Phys. J.. 49, 195 (2006).
A. K. Murtazaev and A. B. Babaev, JETP Lett. 99, 535 (2014).
A. B. Babaev and A. K. Murtazaev, JETP Lett. 105, 384 (2017).
H. G. Ballesteros, L. A. Fernández, V. Martin-Mayor, A. Munoz Sudupe, G. Parisi, and J. J. Ruiz-Lorenzo, J. Phys. A: Math. Gen. 30, 8379 (1997).
U. L. Fulco, F. D. Nobre, L. R. da Silva, and L. S. Lucena, Phys. A (Amsterdam, Neth.. 297, 131 (2001).
J.-K. Kim, Phys. Rev.. 53, 3388 (1996).
L. N. Shchur and O. A. Vasilyev, Phys. Rev.. 65, 016107 (2001).
G. S. Iannacchione, G. P. Crawford, S. Zumer, J. W. Doane, and D. Finotello, Phys. Rev. Lett. 71, 2595 (1993).
F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).
J. Adler, A. Brandt, W. Janke, and S. Shmulyian, J. Phys. A: Math. Gen. 28, 5117 (1995).
R. Paredes V. and J. Valbuena, Phys. Rev.. 59, 6275 (1999).
C. Chatelain and B. Berche, Phys. Rev. Lett. 80, 1670 (1998).
A. K. Murtazaev, A. B. Babaev, and G. Ya. Ataeva, Phys. Solid Stat. 57, 1436 (2015).
A. K. Murtazaev, A. B. Babaev, and G. Y. Ataeva, J. Magn. Magn. Mater. 440, 101 (2017).
C. Vasquez and R. Paredes, Condens. Matter Phys. 9, 305 (2006).
C. J. Q. Yin, B. Zheng, and S. Trimper, Phys. Rev.. 72, 036120 (2005).
C. Chatelain, P.-E. Berche, B. Berche, and W. Janke, Nucl. Phys.. 106, 899 (2002).
U. Wolff, Phys. Lett. 62, 361 (1989).
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, and A. H. Teller, J. Chem. Phys. 21, 1087 (1953).
A. B. Babaev and A. K. Murtazaev, Low Temp. Phys. 41, 608 (2015).
A. K. Murtazaev, A. B. Babaev, and G. Ya. Aznaurova, Phys. Solid Stat. 50, 733 (2008).
A. B. Babaev, A. K. Murtazaev, and R. A. Murtazaliev, Solid State Phenom. 233–234, 79 (2015).
A. K. Murtazaev, A. B. Babaev, and G. Ya. Ataeva, Phys. Solid Stat. 59, 141 (2017).
K. Eichhorn and K. Binder, J. Phys.: Condens. Matte. 8, 5209 (1996).
N. A. Alves, B. A. Berg, and R. Villanova, Phys. Rev.. 41, 383 (1990).
M. E. Fisher and M. N. Barber, Phys. Rev. Lett. 28, 1516 (1972).
D. Loison, Phys. Lett.. 257, 83 (1999).
P. Peczac, A. M. Ferrenberg, and D. P. Landau, Phys. Rev.. 43, 6087 (1991).
O. A. Vasilyev and L. N. Shchur, J. Exp. Theor. Phys. 90, 964 (2000).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.B. Babaev, A.K. Murtazaev, 2018, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2018, Vol. 107, No. 10, pp. 656–661.
Rights and permissions
About this article
Cite this article
Babaev, A.B., Murtazaev, A.K. Weak Universality in the Disordered Two-Dimensional Antiferromagnetic Potts Model on a Triangular Lattice. Jetp Lett. 107, 624–628 (2018). https://doi.org/10.1134/S0021364018100053
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364018100053