First excitations in two- and three-dimensional random-field Ising systems

TL;DR

This study investigates the first excited states in 2D and 3D random-field Ising models using an improved exact algorithm, revealing phase transition signatures and fractal properties of excitations.

Contribution

It introduces a corrected algorithm for accurately finding first excited states and analyzes their behavior across phase transitions in random-field Ising systems.

Findings

Phase transition in 3D evidenced by excitation energy crossings.

Fractal dimension of excitations in 3D is approximately 2.42.

In 2D, excitations vanish at zero disorder, indicating no finite-temperature transition.

Abstract

We present results on the first excited states for the random-field Ising model. These are based on an exact algorithm, with which we study the excitation energies and the excitation sizes for two- and three-dimensional random-field Ising systems with a Gaussian distribution of the random fields. Our algorithm is based on an approach of Frontera and Vives which, in some cases, does not yield the true first excited states. Using the corrected algorithm, we find that the order-disorder phase transition for three dimensions is visible via crossings of the excitations-energy curves for different system sizes, while in two-dimensions these crossings converge to zero disorder. Furthermore, we obtain in three dimensions a fractal dimension of the excitations cluster of d_s=2.42(2). We also provide analytical droplet arguments to understand the behavior of the excitation energies for small and large disorder as well as close to the critical point.