By Philip Phillips

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Similar to standard liquid–gas systems, the coexistence region and the associated ﬁrst-order line terminate at the critical end-point at T = Tc . , 2003a) on chromiumdoped V2 O3 , and was found to belong to the standard Ising universality class. Weak disorder near Mott transitions All quantities display a discontinuity across any ﬁrst-order phase transition, but this jump can be reduced in the presence of impurities or disorder, which tend to locally favor one or the other phase. Well-known droplet arguments (Imry and Ma, 1975) then suggest that suﬃciently strong disorder can completely suppress such a ﬁrstorder transition (Berker, 1991), eliminating the ﬁnite-temperature metal–insulator coexistence region.

When disorder is added, each of these energy levels is shifted by a randomly ﬂuctuating site energy −W/2 < εi < W/2. The situation remains unchanged for W < U , as all the levels ε1 (i) = U + εi remain empty (for half-ﬁlling the chemical potential is μ = EF = U/2). For larger disorder, those sites with εi > U/2 have the level ε0 (i) = 0 + εi > μ and are empty. Similarly, those sites with εi < −U/2 have the excited level ε1 (i) = U + εi < μ and are doubly occupied. Thus for W > U a fraction of the sites are either doubly occupied or empty.

1979) may be viewed as a convenient phenomenological description of how the conductance depends on length scale. While its implicit assumptions prove correct for the problem of Anderson localization of non-interacting electrons, one may ask the same question for other models of the MIT. In particular, the percolation problem represents a consistent description of the transition in the semiclassical limit. Since percolation (Stauﬀer and Aharoni, 1994) is a well-characterized (classical) critical phenomenon, power-law scaling of all quantities is still valid, and many of the same questions raised by the “gang of four” can be again posed.