Fractons with Scalar and Vector Interactions and Two Scaling Relations between the Static and Dynamic Critical Exponents

Abstract

Using new equilibrium equation [PhysicaA242, 13 (1997)] and Einstein's relation, new critical exponents for Young modulus Y(p)∝(p-p c )2t-g and regular diffusion [Formula: see text] are introduced, where t is the conductivity critical exponent and g=0.6 is the Hall coefficient critical exponent above the threshold. These results allows us to introduce two superuniversal fractons dimensions: with the scalar displacements d s =4/3 (the Alexander and Orbach conjecture) and with the vector displacements d v =21/20) which leads to new scaling relations between the static and dynamic critical exponents: t=1/2[(3d-4)ν-g]; t=[2ν(20d-21)+21g+2β)/42 in all (3≼d≼6) space dimensions.