Abstract
We present results on the first excited states for the random-field Ising model. These arebased on an exact algorithm, with which we study the excitation energies and theexcitation sizes for two- and three-dimensional random-field Ising systems with a Gaussiandistribution of the random fields. Our algorithm is based on an approach of Frontera andVives which, in some cases, does not yield the true first excited states. Using the correctedalgorithm, we find that the order–disorder phase transition for three dimensions isvisible via crossings of the excitation 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 excitation cluster ofds = 2.42(2). We also provide analytical droplet arguments to understand the behavior of theexcitation energies for small and large disorder as well as close to the criticalpoint.
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