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A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa'
oleh: R. Kenna, B. Berche
| Format: | Article |
|---|---|
| Diterbitkan: | Institute for Condensed Matter Physics 2013-06-01 |
Deskripsi
It is well known that standard hyperscaling breaks down above the upper critical dimension d<sub>c</sub>, 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<sub>c</sub> they are related algebraically through a new critical exponent coppa, while at d<sub>c</sub> 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.