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The effect of randomness on critical behavior is a crucial subject in condensed matter physics due to the the presence of impurity in any real material. We presently probe the critical behaviour of the antiferromagnetic (AF) Ising model on rewired square lattices with random connectivity. An extra link is randomly added to each site of the square lattice to connect the site to one of its next-nearest neighbours, thus having different number of connections (links). Average number of links (ANOL) $kappa$ is fractional, varied from 2 to 3, where $kappa = 2$ associated with the native square lattice. The rewired lattices possess abundance of triangular units in which spins are frustrated due to AF interaction. The system is studied by using Monte Carlo method with Replica Exchange algorithm. Some physical quantities of interests were calculated, such as the specific heat, the staggered magnetization and the spin glass order parameter (Edward-Anderson parameter). We investigate the role played by the randomness in affecting the existing phase transition and its interplay with frustration to possibly bring any spin glass (SG) properties. We observed the low temperature magnetic ordered phase (Neel phase) preserved up to certain value of $kappa$ and no indication of SG phase for any value of $kappa$.
Spin glass (SG) is a typical magnetic system with frozen random spin orientation at low temperatures. The system exhibits rich physical properties, such as infinite number of ground states, memory effect and aging phenomena. There are two main ingred
We investigate the critical properties of the Ising model in two dimensions on {it directed} small-world lattice with quenched connectivity disorder. The disordered system is simulated by applying the Monte Carlo update heat bath algorithm. We calcul
For the 2D Ising model, we analyzed dependences of thermodynamic characteristics on number of spins by means of computer simulations. We compared experimental data obtained using the Fisher-Kasteleyn algorithm on a square lattice with $N=l{times}l$ s
The site-diluted transverse field Ising model in two dimensions is studied with Quantum-Monte-Carlo simulations. Its phase diagram is determined in the transverse field (Gamma) and temperature (T) plane for various (fixed) concentrations (p). The nat
We study critical behavior of the diluted 2D Ising model in the presence of disorder correlations which decay algebraically with distance as $sim r^{-a}$. Mapping the problem onto 2D Dirac fermions with correlated disorder we calculate the critical p