Dimensional reduction in entropy dominated transitions with possible application to short-range spin-glasses

Abstract

The author studies from general considerations, the critical behaviour of systems which condense, at their critical temperature Tc, into a weakly coherent critical state with an infinitely large number of weakly coherent critical state with an infinitely large number of internal degrees of freedom. If this number (per volume of size xi d where xi is the correlation length) varies as xi rho with 0< rho <d, the reduced dimension d=d- rho is naturally associated with the extremely large fluctuations at the transition. Assuming that xi approximately (T-Tc)- nu with nu = nu (d) of some regular d-dimensional model, the negative value of the specific-heat exponents alpha = alpha (d)- rho nu follows. He proposes a relation between rho and other critical exponents and compute self-consistently the dimensional reduction. The short-range Ising spin glass below an intermediate critical dimensionality (probably dicd=4) may provide a realisation of such an entropy-dominated transition. If all frustration effects are accounted for by the effective shift in dimensionality, the following consequences are anticipated: (i) The lower critical dimension is dlcd=2. (ii) The 3d exponents are nu SG=1 and alpha SG=-1. These conjectures agree surprisingly well with several recent numerical simulations.