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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.

In this paper we have presented computational results for excitations of ground states for the Villain model [

We have expected the Villain model to have a spin glass at zero temperature in the aforementioned limit of weak disorder. In this study, the square lattice

An outline of this paper is as follows. In Section 2 we introduce formalism and discuss with model and method how one can calculate first excitations. In Section 3 we present results from numerical simulation of the Villain model with antiferromagnetic exchange randomness and in Section 4 we draw concluding remarks.

The frustration of two dimensional Ising model with interaction in one dimension is studied in this paper extensively. The two dimensional fully frustrated Ising model, or Villain model [

where

The method is used in the calculation basing on the Pfaffian [

where

where r is an integer and X is a real number. At T = 0 there is a degeneracy at

where

The specific heat of the system can be written as

We have carried out a numerical calculation to lift degeneracies of excited states at zero temperature. The disorder is confined to a frustrated square patch with periodic boundary conditions in one dimension. Square lattices of size

are the most likely value in the scale

We have carried out a numerical study of the Villain model, showing that there is an observation that indicates a zero temperature spin glass phase with weak disorder. We have used a computer code that is able to collect numerical data for simulation. The Pfaffian approach is used to collect data for first excitations of ground states, based on perturbation theory. It has been observed clearly that the spin glass phase occurs at concentration of defect bonds

The authors are grateful to the authority of Chittagong University of Engineering and Technology (CUET). The authors also would like to thanks Professor Dr. Julian Poulter for valuable advise during the research work.