Abstract
This article presents a summary of recent studies of quantum phase transitions in random magnets using Monte Carlo methods. The quantum Ising model with random interactions in the presence of a transverse magnetic field is used as a primary example of a quantum phase transition driven by the strength of the applied field. After a brief discussion of experimental results and analytical results in one-dimension, results of numerical Monte Carlo simulations on the quantum critical behavior of the nearest neighbor Ising spin glass in two and three dimensions, as well as the random Ising ferromagnet in two dimensions are described in detail. Rare fluctuations of the quenched random bond distribution are found to have an important effect on the response of the system in the vicinity of the quantum phase transition, and are found to lead to divergent response in the paramagnetic phase itself. Such nonuniversal behavior is exhibited by many quantum models with quenched randomness; their effect on the description of the quantum phase transition is briefly discussed.
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Bhatt, R.N. (1998). Quantum Phase Transitions in Random Magnets. In: Landau, D.P., Mon, K.K., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics X. Springer Proceedings in Physics, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46851-3_7
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