A new critical exponent (sic) and its logarithmic counterpart (sic)

作者：Kenna R^*; Berche B

来源：Condensed Matter Physics, 2013, 16(2): UNSP 23601.

DOI：10.5488/CMP.16.23601

• hyperscaling
• critical dimension
• correlation length
• critical exponents
• scaling relations

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 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 (sic), while at d(c) they differ through logarithmic corrections governed by an exponent %26lt;((sic))over cap%26gt;.Taking proper account of these different length scales allows one to extend hyperscaling to all dimensions.

• 出版日期2013