- Access by Xinjiang University
Phase diagram and critical exponent for the nearest-neighbor and next-nearest-neighbor interaction Ising model
Phys. Rev. E 76, 021123 – Published 29 August, 2007
DOI: https://doi.org/10.1103/PhysRevE.76.021123
Abstract
We obtain an approximation of the phase diagram of an Ising model with both nearest-neighbor and next-nearest-neighbor interactions on the square lattice. We use the Fisher zeros of the partition functions of a sequence of finite-sized systems along with various extrapolation methods to obtain phase transition points. In addition, we obtain an approximate value of the correlation length critical exponent . Our results are compared to previous results for this system using a wide variety of other approaches.
Article Text
References (27)
- L. Onsager, Phys. Rev. 65, 117 (1944).
- N. W. Dalton and D. W. Wood, J. Math. Phys. 10, 1271 (1969).
- J. Oitmaa, J. Phys. A 14, 1159 (1981).
- J. Oitmaa and M. J. Velgakis, J. Phys. A 20, 1269 (1987).
- T. W. Burkhardt, Z. Phys. B 29, 129 (1978).
- M. Nauenberg and B. Nienhuis, Phys. Rev. Lett. 33, 944 (1974).
- M. P. Nightingale, Phys. Lett. 59, 486 (1977).
- R. H. Swendsen and S. Krinsky, Phys. Rev. Lett. 43, 177 (1979).
- M. P. Nightingale and H. W. J. Blote, Physica A 251, 211 (1998).
- D. P. Landau, Phys. Rev. B 21, 1285 (1980).
- K. Binder and D. P. Landau, Phys. Rev. B 21, 1941 (1980).
- D. P. Landau and K. Binder, Phys. Rev. B 31, 5946 (1985).
- H. W. J. Blote, A. Compagner, and A. Hoogland, Physica A 141, 375 (1987).
- A. N. Berker and K. Hui, Phys. Rev. B 48, 12393 (1993).
- K. Minami and M. Suzuki, Physica A 195, 457 (1993).
- H. J. W. Zandvliet, Europhys. Lett. 73, 747 (2006).
- A. Malakis, P. Kalozoumis, and N. Tyraskis, Eur. Phys. J. B 50, 63 (2006).
- C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (1952); 87, 410 (1952).
- S.-Y. Kim, Phys. Rev. Lett. 93, 130604 (2004).
- R. J. Creswick, Phys. Rev. E 52, R5735 (1995).
- K. Binder, Physica (Amsterdam) 62, 508 (1972).
- G. Bhanot, J. Stat. Phys. 60, 55 (1990).
- R. Bulirsch and J. Stoer, Numer. Math. 6, 413 (1964).
- M. Henkel and A. Patkos, J. Phys. A 20, 2199 (1987).
- J. L. Monroe, Phys. Rev. E 65, 066116 (2002).
- M. P. Nightingale and H. W. J. Blote, J. Phys. A 15, L33 (1982).
- C. Itzykson, R. B. Pearson, and J. B. Zuber, Nucl. Phys. B 220, 415 (1983).