It is well known that standard hyperscaling breaks down above the upper critical dimension dc, 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 correlationlength scale and the underlying length scale of the system are not the same at or above the upper critical dimension. Above dc they are related algebraically through a new critical exponent 'coppa' , while at dc they differ through logarithmic corrections governed by an exponent 'hat coppa'. Taking proper account of these different length scales allows one to extend hyperscaling to all dimensions.
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- correlation length
- critical dimension
- critical exponents
- scaling relations