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Infinite-randomness quantum Ising critical fixed points

Motrunich, Olexei and Mau, Siun-Chuon and Huse, David A. and Fisher, Daniel S. (2000) Infinite-randomness quantum Ising critical fixed points. Physical Review B, 61 (2). pp. 1160-1172. ISSN 0163-1829.

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We examine the ground state of the random quantum Ising model in a transverse field using a generalization of the Ma-Dasgupta-Hu renormalization group (RG) scheme. For spatial dimensionality d=2, we find that at strong randomness the RG flow for the quantum critical point is towards an infinite-randomness fixed point, as in one dimension. This is consistent with the results of a recent quantum Monte Carlo study by Pich et al. [Phys. Rev. Lett. 81, 5916 (1998)], including estimates of the critical exponents from our RG that agree well with those from the quantum Monte Carlo. The same qualitative behavior appears to occur for three dimensions; we have not yet been able to determine whether or not it persists to arbitrarily high d. Some consequences of the infinite-randomness fixed point for the quantum critical scaling behavior are discussed. Because frustration is irrelevant in the infinite-randomness limit, the same fixed point should govern both ferromagnetic and spin-glass quantum critical points. This RG maps the random quantum Ising model with strong disorder onto a novel type of percolation/aggregation process.

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Motrunich, Olexei0000-0001-8031-0022
Additional Information:© 2000 The American Physical Society. Received 21 June 1999. We thank Ravin Bhatt, Kedar Damle, Matthew Hastings, and Peter Young for helpful discussions. Support for this work was provided by the National Science Foundation through Grants No. DMR-9400362, No. DMR-9630064, and No. DMR-9802468 and Harvard’s MRSEC.
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Deposited On:09 Jan 2007
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