Spin Glass Phase Exists in the Random Weak Disorder for the Villain Model

Sunil  Dhar; Md. Yeakub  Ali

doi:10.4236/jamp.2014.213139

Md. Yeakub Ali^*, Sunil Dhar

Abstract: In this work we have studied non random Villain model by introducing simple defects to calculate degeneracies of the first excited states using Pfaffian approach through a perturbation theory. The distributions of excitations of the ground states are displayed graphically. The results are indicated that spin glass occurs in the weak disorder for the Villain model. At the concentration of defect bonds p=0.03, the distribution behaves in the same manner as for p=0.5 for different sizes of lattice. The latest result of the spin glass is presented in this paper.

Keywords: Spin Glass, First Excitations, Distribution, Square Lattice

Cite this paper: Ali, M. and Dhar, S. (2014) Spin Glass Phase Exists in the Random Weak Disorder for the Villain Model. Journal of Applied Mathematics and Physics, 2, 1190-1195. doi: 10.4236/jamp.2014.213139.

References

[1] Villain, J. (1977) Spin Glass with Non-Random Interactions. Journal of Physics C: Solid State Physics, 10, 1717.
http://dx.doi.org/10.1088/0022-3719/10/10/014

[2] Ali, M.Y. and Poulter, J. (2013) Spin Correlation Function of the Fully Frustrated Ising Model and ±J Ising Spin Glass on the Square Lattice. Chinese Physics B, 22, Article ID: 067502.
http://dx.doi.org/10.1088/1674-1056/22/6/067202

[3] Mezard, M., et al. (1987) Spin Glass Theory and Beyond. World Scientific, Singapore.

[4] Atisattapong, W. and Poulter, J. (2008) Energy Gap of the Bimodal Two-Dimensional Ising Spin Glass. New Journal of Physics, 10, Article ID: 093012.
http://dx.doi.org/10.1088/1367-2630/10/9/093012

[5] Jinuntuya, N. and Poulter, J. (2012) Elementary Excitations and the Phase Transition in the Bimodal Ising Spin Glass Model. Journal of Statistical Mechanics: Theory and Experiment, 2012, Article ID: P01010.
http://dx.doi.org/10.1088/1742-5468/2012/01/P01010

[6] Blackman, J.A. and Poulter, J. (1991) Gauge-Invariant Method for the ±J Spin-Glass Model. Physical Review B, 44, 4374.
http://dx.doi.org/10.1103/PhysRevB.44.4374

[7] Katzgraber, H.G., et al. (2007) Effective Critical Behavior of the Two Dimensional Ising Spin Glass with Bimodal Interaction. Physical Review B, 75, Article ID: 014412.

[8] Kac, M. and Ward, J.C. (1952) A Combinatorial Solution of the Two Dimensional Ising Model. Physical Review, 88, 1332.
http://dx.doi.org/10.1103/PhysRev.88.1332

[9] Green, H.S. and Hurst, C.A. (1964) Order-Disorder Phenomena. In-Terscience, London.

[10] Blackman, J.A. and Poulter, J. (1982) Two-Dimensional Frustrated Ising Network as an Eigenvalue Problem. Physical Review B, 26, 4987.
http://dx.doi.org/10.1103/PhysRevB.26.4987

[11] Wang, J.S. and Swendens, R.H. (1988) Monte Carlo Renormalization Group Study of Ising Spin Glasses. Physical Review B, 38, 4840.
http://dx.doi.org/10.1103/PhysRevB.37.7745

[12] Fischer, K.S. and Hertz, J.A. (1991) Spin Glasses. Cambridge University Press, London.
http://dx.doi.org/10.1017/CBO9780511628771

[13] Stein, D. (1992) Spin Glasses and Biology. World Scientific, Singapore.
http://dx.doi.org/10.1142/0446

[14] Sherrington, D. Spin Glasses. Preprint: cond-mat/9806289

[15] Pathria, R.K. (1972) Statistical Mechanics. Pergamon Press, New York.