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The effect of randomness on critical behavior is a crucial subject incondensed matter physics due to the the presence of impurity in any realmaterial. We presently probe the critical behaviour of the antiferromagnetic(AF) Ising model on rewired square lattices with random connectivity. An extralink is randomly added to each site of the square lattice to connect the siteto one of its next-nearest neighbours, thus having different number ofconnections (links). Average number of links (ANOL) $\kappa$ is fractional,varied from 2 to 3, where $\kappa = 2$ associated with the native squarelattice. The rewired lattices possess abundance of triangular units in whichspins are frustrated due to AF interaction. The system is studied by usingMonte Carlo method with Replica Exchange algorithm. Some physical quantities ofinterests were calculated, such as the specific heat, the staggeredmagnetization and the spin glass order parameter (Edward-Anderson parameter).We investigate the role played by the randomness in affecting the existingphase transition and its interplay with frustration to possibly bring any spinglass (SG) properties. We observed the low temperature magnetic ordered phase(N\'eel phase) preserved up to certain value of $\kappa$ and no indication ofSG phase for any value of $\kappa$.

Critical properties of the antiferromagnetic Ising model on rewired square lattices