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Title
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On the range of validity of a semiclassical relation between the critical exponents at the Anderson localization transition
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Author
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Abstract
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| Using Wegner's result relating critical exponents s and ν for conductivity and localization length, respectively, via dimensionality d and that for ν given by García-García, we derive what we term a semiclassical (sc) relation for ν in terms of s, which is independent of dimensionality. Forming the ratio s/ν versus d from the above relations, s/ν=0 at d=2 is due to a singularity in the sc relation for ν. We argue that, in reality, s/ν=0 results from s being zero at d=2. Finally we conjecture that (i) Wegner's prediction s/ν=1 when d=3 and (ii) ν tends to 1/2 at large s, are both insensitive to interactions. |
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Language
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English
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Source (journal)
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The journal of physics and chemistry of solids. - New York, N.Y.
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Publication
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New York, N.Y.
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2011
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ISSN
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0022-3697
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DOI
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10.1016/J.JPCS.2011.09.012
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Volume/pages
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72
:12
(2011)
, p. 1529-1531
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ISI
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000297394500025
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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