A new critical exponent koppa and its logarithmic counterpart koppa-hat
Abstract
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.
Keywords
Cite
@article{arxiv.1411.2754,
title = {A new critical exponent koppa and its logarithmic counterpart koppa-hat},
author = {R. Kenna and B. Berche},
journal= {arXiv preprint arXiv:1411.2754},
year = {2014}
}
Comments
Invited contribution to a special edition of CMP: Phase transitions and critical phenomena: universality and non-universal features. 13 pages, 6 figures