  It is well known that standard hyperscaling breaks down above the upper
critical dimension d_c, where the critical exponents take on their Landau
values. Here we show that this is because, in standard formulations in the
thermodynamic limit, distance is measured on the correlation-length scale.
However, the correlation-length scale and the underlying length scale of the
system are not the same at or above the upper critical dimension. Above d_c
they are related algebraically through a new critical exponent koppa, while at
d_c they differ through logarithmic corrections governed by an exponent
koppa-hat. Taking proper account of these different length scales allows one to
extend hyperscaling to all dimensions.

Statistical Mechanics