The results are summarised in table 1. All these results
have been calculated in the middle of the band (i.e. ), but there
is ample evidence that for the models considered here, this point is
not special and is truly representative of the whole band, at least in the
range
.
Table 1:
N.B: The estimates of and
are based on the values
given by several different fitting procedures.
Unlike previous calculations (Kramer et al. 1990) the exponents calculated for the two distributions now overlap well and are therefore consistent with the common assumption that simply changing the distribution does not change the universality class and hence the critical exponent. The discrepancy reported previously is presumably due to insufficient accuracy in the raw data and consequent assumption of a critical range of disorder which was too wide.
This may have consequences for experiment as it seems to suggest that it is possible to obtain an exponent of unity simply by using too wide a range of data around the critical disorder, energy, pressure, etc. It should also be borne in mind that the influence of interactions may also account for differences between experimental results and those based on a model of non-interacting electrons. For this reason it may be more realistic to compare the present results with photonic or acoustic rather than electronic experiments.
In summary, the critical exponent of the Anderson model of the
metal-insulator transition is .