The Random Transverse Field Ising Ferromagnet: the Simplest Disordered Model with a Quantum Phase Transition

A.P. Young and C. Pich

After an introduction to quantum phase transitions, we study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one-dimension: the dynamical exponent is infinite and, at the critical point, the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point, there may be different exponents for the divergence of the average and typical correlation lengths, again as in one-dimension, but the evidence for this is less strong.

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