SPIN-WAVE DYNAMICS OF PERCOLATING HEISENBERG ANTIFERROMAGNETS

The fracton dynamics of percolating Heisenberg antiferromagnets are st udied in terms of a dynamic scaling argument and large-scale numerical analysis. It is shown that the spectral (or fracton) dimension for an tiferromagnetic fractons, ($) over tilde d(AF), is bounded by the rela tion ($) over tilde d(AF)less than or equal to 1. The densities of sta tes (DOS) are calculated for very large percolating antiferromagnets a t the critical concentration p(c) formed on d=2, 3, and 4 simple cubic lattices. It is concluded, from the calculated DOS's, that the spectr al dimensions ($) over tilde d(AF) are very close to unity for any Euc lidean dimension d(greater than or equal to 2). We have also calculate d the DOS for percolating antiferromagnets above p(c) in order to clar ify the crossover behavior from extended magnons to fractons. In addit ion, the dynamical structure factor S(q, omega) is investigated both a nalytically and numerically. It is found, postulating a single-length scaling, that the asymptotic behaviors can be characterized by two exp onents, the dynamical exponent Z(AF) and a new exponent y. The numeric al results for S(q, omega) support the validity of the single-length-s cale postulate.