TY - JOUR

T1 - The mobility edge as a spin-glass problem

AU - Aharony, Amnon

AU - Imry, Yoseph

PY - 1977

Y1 - 1977

N2 - An analogy is considered between long-range properties of the Green function G of an electron moving in a random potential, near the mobility edge, and those of spin-spin correlation functions, obtained for a random Ginzburg-Landau Gaussian model. The absence of a 'ferromagnetic' long-range order in the latter model is related to the short range of the average G. The average squared modulus may become long ranged. This long range is analogous to a 'spin-glass' like phase. This 'spin-glass' transition deviates from mean-field theory for dimensionalities d<4. Renormalisation group, the epsilon expansion and the n to 0 replica trick are used to analyse the appropriate fixed points. For few impurities, no fixed point can be reached, probably because no localisation edge exists. For larger disorder, the 'isotropic', n=0 fixed point may be reached, and is interpreted as probably leading to percolation. For still larger disorder, the Anderson transition may result.

AB - An analogy is considered between long-range properties of the Green function G of an electron moving in a random potential, near the mobility edge, and those of spin-spin correlation functions, obtained for a random Ginzburg-Landau Gaussian model. The absence of a 'ferromagnetic' long-range order in the latter model is related to the short range of the average G. The average squared modulus may become long ranged. This long range is analogous to a 'spin-glass' like phase. This 'spin-glass' transition deviates from mean-field theory for dimensionalities d<4. Renormalisation group, the epsilon expansion and the n to 0 replica trick are used to analyse the appropriate fixed points. For few impurities, no fixed point can be reached, probably because no localisation edge exists. For larger disorder, the 'isotropic', n=0 fixed point may be reached, and is interpreted as probably leading to percolation. For still larger disorder, the Anderson transition may result.

UR - http://www.scopus.com/inward/record.url?scp=0005500698&partnerID=8YFLogxK

U2 - 10.1088/0022-3719/10/17/005

DO - 10.1088/0022-3719/10/17/005

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AN - SCOPUS:0005500698

SN - 0022-3719

VL - 10

SP - L487-L492

JO - Journal of Physics C: Solid State Physics

JF - Journal of Physics C: Solid State Physics

IS - 17

M1 - 005

ER -