Condensed Matter Physics, 2013, vol. 16, No. 2, 23601:112
DOI:10.5488/CMP.16.23601
Title:
A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa'
Author(s):

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 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 correlationlength 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 d_{c} they are related algebraically
through a new critical exponent \coppa, while at d_{c} 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,64.60.an,05.50.+q,64.60.De,11.10.Kk
