Critical properties of the antiferromagnetic Ising model on rewired square lattices

TL;DR

This study investigates how random connectivity in rewired square lattices affects the critical behavior of the antiferromagnetic Ising model, revealing preserved magnetic order but no spin glass phase across various levels of randomness.

Contribution

It introduces a model with variable random connectivity in square lattices and analyzes its critical properties using Monte Carlo simulations, highlighting the effects of frustration and randomness.

Findings

Néel phase persists up to a certain randomness level.

No evidence of spin glass phase at any connectivity.

Random rewiring influences critical behavior without inducing spin glass order.

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) $\kappa$ 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 (N\'eel phase) preserved up to certain value of $\kappa$ and no indication of SG phase for any value of $\kappa$.