DERIVATION OF CRITICAL EXPONENTS FROM EXTREME VALUE DISTRIBUTIONS

It is shown that all critical exponents, with the exception of the hea t capacity exponent other than for the mean field theory, can be deriv ed from the characteristic exponent of an extreme value distribution f or the smallest value and the dimensionality of the space. The relatio n between the characteristic exponent and the dimensionality d of the space imposes the condition d less-than-or-equal-to 4. This is borne o ut by direct evaluation of the spatial correlation function.