Random-bond antiferromagnetic Ising model in a field

TL;DR

This study investigates the critical behavior of 2D and 3D random-bond antiferromagnetic Ising models in a field using combinatorial optimization, revealing mixed-order transitions in 2D and ambiguous order in 3D.

Contribution

It provides the first detailed analysis of the critical properties of the random-bond antiferromagnetic Ising model in a field in both two and three dimensions.

Findings

2D transition is mixed order with specific critical exponents.

3D transition has exponents compatible with the random-field Ising model.

Transition order in 3D remains ambiguous between second and mixed order.

Abstract

Using combinatorial optimisation techniques we study the critical properties of the two- and the three-dimensional Ising model with uniformly distributed random antiferromagnetic couplings $(1 \le J_i \le 2)$ in the presence of a homogeneous longitudinal field, $h$, at zero temperature. In finite systems of linear size, $L$, we measure the average correlation function, $C_L(\ell,h)$, when the sites are either on the same sub-lattice, or they belong to different sub-lattices. The phase transition, which is of first-order in the pure system, turns to mixed order in two dimensions with critical exponents $1/\nu \approx 0.5$ and $\eta \approx 0.7$. In three dimensions we obtain $1/\nu \approx 0.7$, which is compatible with the value of the random-field Ising model, but we cannot discriminate between second-order and mixed-order transitions.