Abstract
This work investigates the square lattice in the presence of an-ti-ferromagnetic exchange considering the two-dimensional Ising Villain model. A computational scheme is constructed to evaluate the degeneracy of ground states at zero temperature employing the Pfaffian method through perturbation theory. The entropy and canonical spin glass of the considered model are precisely obtained. The critical point between the Villain phase and canonical spin glass phase with the line fit of entropy at the thermodynamic limit is investigated. It is also shown that the transition point of the Villain model lies in the low concentration regime.
Highlights
It is well established that the two-dimensional Ising model is one of the leading non-trivial models, which divulge an exact solution and is widely used for describing physical phenomena in statistical physics
This work investigates the square lattice in the presence of anti-ferromagnetic exchange considering the two-dimensional Ising Villain model
Being motivated above the discussion, the purpose of this paper is to present some computational results for the critical behavior of the Villain model [22] brought about in a two-dimensional fully frustrated Ising system by introducing ferromagnetic defects
Summary
It is well established that the two-dimensional Ising model is one of the leading non-trivial models, which divulge an exact solution and is widely used for describing physical phenomena in statistical physics. The problems of disordered systems can be studied through the early formulation considered, the perfect Ising lattice by employing the technique. The frustration plays a vital role as a key element to study the disordered system, the socalled spin-glass problem [1]. It may arise from the geometry of the lattice or from a quenched random distribution of positive (ferromagnetic) and negative (anti-ferromagnetic) bonds. One of the canonical models of frustrated systems is the two-dimensional Ising model. A large number of authors [2]-[7] have studied the canonical model with p = 0.5 on a square lattice considering various assumption.
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