Detailed magnetization study of quenched random ferromagnets. II. Site dilution and percolation exponents.

Abstract

We report the experimental determination of the crossover exponent (\ensuremath{\varphi}) and the percolation critical exponents for magnetization (${\mathrm{\ensuremath{\beta}}}_{\mathit{p}}$) and spin-wave stiffness (\ensuremath{\theta}) for quench-disordered (amorphous) three-dimensional (d=3) dilute Heisenberg ferromagnets. The values of \ensuremath{\varphi}, \ensuremath{\theta}, and ${\mathrm{\ensuremath{\beta}}}_{\mathit{p}}$, so obtained, as well as those of the percolation correlation-length critical exponent ${\ensuremath{\nu}}_{\mathit{p}}$ and the conductivity exponent \ensuremath{\sigma}, deduced from the exponent equalities ${\ensuremath{\nu}}_{\mathit{p}}$=\ensuremath{\varphi}-(\ensuremath{\theta}/2) and \ensuremath{\sigma}=(d-2)${\ensuremath{\nu}}_{\mathit{p}}$+\ensuremath{\varphi}, conform very well with the most accurate theoretical estimates published recently. A comparison of the presently determined exponent values with those theoretically predicted for site or bond percolation on a d=3 crystalline lattice asserts that the critical behavior of percolation on a regular d=3 lattice does not get altered in the presence of quenched randomness if the specific-heat exponent of the regular system is negative. Consistent with the Alexander-Orbach conjecture (Golden inquality), the fracton dimensionality d\ifmmode\bar\else\textasciimacron\fi{}\ifmmode\bar\else\textasciimacron\fi{} of the percolating cluster at threshold (the conductivity exponent \ensuremath{\sigma}) turns out to be d\ifmmode\bar\else\textasciimacron\fi{}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\simeq}4/3 (\ensuremath{\sigma}\ensuremath{\le}2). The present results vindicate the universality hypothesis.