
TY  - JOUR
A1  - Buckingham, MJ 
T1  - Correlations, Long Range Order and Dimensionality
JF  - Australian Journal of Physics
JO  - Aust. J.  Phys.
Y1  - 1983
VL  - 36
IS  - 5
SP  - 683
EP  - 700
KW  - 
UR  - https://doi.org/10.1071/PH830683 
N2  - After a retrospective look at the nature of correlations in the case of the helium A transition, we consider long range correlations and their information content for critical phenomena in general. Separation of the statistical from the geometric information leads to the resolution of a long-standing dilemma concerning the dimensionality dependence of the hyper-scaling relations. The hyper-scaling inequalities are the result of the significant correlations suffering a re-arrangement when a regular contribution dominates the singular part of the free energy. The inequalities can each be replaced by a pair of equalities. This resolution has a bearing on the special place of four dimensions as the origin for the e-expansion technique of the renormalization group approach. 
ER  -

