Condensed Matter Physics, 2013, vol. 16, No. 2, 23601:1-12

Title: A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa'
  R. Kenna (Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, England) ,
  B. Berche (Statistical Physics Group, Institut Jean Lamour, UMR CNRS 7198, Universite de Lorraine, B.P. 70239, 54506 Vandoe uvre les Nancy Cedex, France)

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 correlation-length 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.

Key words: hyperscaling, critical dimension, correlation length, critical exponents, scaling relations
PACS: 64.60.-i,,05.50.+q,64.60.De,11.10.Kk

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