Author(s)

Md. Yeakub Ali^*, Sunil Dhar

Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong, Bangladesh.

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.

Spin Glass, First Excitations, Distribution, Square Lattice

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.