Anomalous finite size corrections in random field models

Abstract

The presence of a random magnetic field in ferromagnetic systems leads, in the broken phase, to an anomalous $O(\sqrt{1/N})$ convergence of some thermodynamic quantities to their asymptotic limits. Here we show a general method, based on the replica trick, to compute analytically the $O(\sqrt{1/N})$ finite size correction to the average free energy. We apply this method to two mean field Ising models, fully connected and random regular graphs, and compare the results to exact numerical algorithms. We argue that this behaviour is present in finite dimensional models as well.

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Cited by in corpus (3)

• Finite size effects in the microscopic critical properties of jammed configurations: A comprehensive study of the effects of different types of disorder
• The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism
• An improved Belief Propagation algorithm finds many Bethe states in the random field Ising model on random graphs