Optimization in random field Ising models by quantum annealing
Matti Sarjala, Viljo Petäjä, Mikko Alava · Journal of Statistical Mechanics Theory and Experiment · 2006
We investigate the properties of quantum annealing applied to the random field Ising model in one, two and three dimensions. The decay rate of the residual energy, defined as the energy excess from the ground state, is found to be e res ∼ log( N MC ) − ζ with ζ in the range 2...6, depending on the strength of the random field. Systems with 'large clusters' are harder to optimize as measured by ζ. Our numerical results suggest that in the ordered phase ζ = 2 whereas in the paramagnetic phase the annealing procedure can be tuned so that ζ → 6.