Abstract. 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) κ is fractional, varied from 2 to 3, where κ = 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 exisiting phase transition and its interplay with frustration to possibly bring any spin glass (SG) properties. We observed the low temperature magnetic ordered phase (Néel phase) preserved up to certain value of κ and no indication of SG phase for any value of κ. IntroductionThe cooperative phenomena are ubiquitous in nature, driven by the presence of coupling interaction between each individual constituent of materials [1,2]. This is exemplified by the spontaneous magnetization by which certain magnetic material is entering a ferromagnetic phase below its transition temperature T c (Curie temperature) and able to attract the nearby metals surrounding it. The high temperature disorded phase and the cooperative ordered phase at low temperature are separated by T c . A phase transition is essentially rendered by the competition between the external fields, such as temperature, which tend to destroy the order and the coupling interaction which tends to create order.Based on the nature of free energy function, a phase transition is grouped into the first and the second order phase transition [3]. The transition is called as first order if the first order derivative of the free energy of the system is discontinuous. If the derivative is continuous, the transition is second order, also called continuous phase transition, at which no latent heat involved in the course of transition and no co-existing phases [2,4]. A firm example of these is the phase transition experienced by PVT systems above the critical point [5]. The phenomena nearby critical point are known as critical phenomena, and affected by limited number of controlling variables such as the type of coupling interaction, symmetry of the microscopic constituents

Abstract. 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 ingredients considered to be pivotal for the existence of SG behavior, namely, frustration and randomness. For the canonical SG system, frustration is led by the presence of competing interaction between ferromagnetic (FM) and antiferromagnetic (AF) couplings. Previously, Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)], reported the SG properties of the AF Ising spins on scale free network (SFN). It is a new type of SG, different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely caused by the topological factor and its randomness is related to the irregular connectvity. Recently, Surungan et. al. [Journal of Physics: Conference Series, 640, 012001 (2015)] reported SG bahavior of AF Heisenberg model on SFN. We further investigate this type of system by studying an AF Heisenberg model on rewired square lattices. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter to search for the existence of SG phase.