Phase transitions and singularities in random quantum systems

Physica A: Statistical Mechanics and its Applications

Volumn 263, Issue 1-4, 1999, Pages 222-233

  Fisher, Daniel S ^a  

^a HARVARD UNIVERSITY   (United States)

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[No Author keywords available]

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EID: 0001111717     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00498-1     Document Type: Article

References (38)

1. Such phenomena in spin glass ordered phases are discussed in D.S. Fisher and D.A. Huse, Phys. Rev B38, 386 (1988).
2. Broad distributions of barriers are found at critical points in classical magnets with a random ordering field, see D.S. Fisher, Phys. Rev. Lett. 56, 416 (1986) and J. Villain, J. Physique, 46, 1843 (1985).
3. Broad distributions of barriers are found at critical points in classical magnets with a random ordering field, see D.S. Fisher, Phys. Rev. Lett. 56, 416 (1986) and J. Villain, J. Physique, 46, 1843 (1985).
4. In disordered phases, see e.g. M. Randeria, J.P. Sethna and R.G. Palmer, Phys. Rev. Lett. 54, 1321 (1985).
5. D.S. Fisher, J. Appl. Phys.61, 3672 (1987).
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7. S-C Mau, O. Motrunich, D.A. Huse and D.S. Fisher, in preparation
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10. A good discussion of this behavior at classical random critical points is in A.W.W. Ludwig, Nuc. Phys. B330, 639 (1990).
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27. D.A. Huse, private communication.
28. A different type of disordered random quantum phase was found in one dimension by: E. Westerberg, A. Furusaki, M. Sigrist and P.A. Lee, Phys. Rev. Lett. 75, 4302 (1982).
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32. For an introduction, see, e.g. D.S. Fisher, in Proceedings of NATO Advanced Study Institute Phase Transitions and Relaxation in Systems with Competing Energy Scales, T. Riste and D. Sherrington, eds., Kluwer (Amsterdam 1993) and references therein.
33. F. Iglói and H. Rieger, Phys. Rev. B57, 11404 (1998) and Phys. Rev. Lett. 78, 2473 (1997).
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35. T. Senthil and S. Sachdev, Phys. Rev. Lett. 77, 5292 (1996) showed that infinite randomness critical points also exist in several rather special circumstances in dimensions d > 1.
36. -z scaling from simulations of the 1-d random quantum Ising model but larger systems show tunneling scaling. [15, 17, 29]
37. See e.g., A.H. Castro-Neto, G. Castillo and B. Jones, cond-mat/9710123.
38. D. Belitz and T. Kirkpatrick, Phys. Rev. B52, 13922 (1995).