Abstract: Treating the randomly Fe-substituted optimally hole-doped manganite La0.7Pb0.3(Mn1?yFey )O3 (y = 0.2,0.3) as a test case, we demonstrate that a combined investigation of both odd and even harmonics of the ac magnetic response permits an unambiguous distinction between the canonical and cluster spin glasses. As expected for a spin glass (SG), the nonlinear ac magnetic susceptibilities ?3(T,?) and ?5(T,?) (odd harmonics) diverge at the SG freezing temperature Tg = 80.00(3) K [Tg = 56.25(5) K] in the static limit and, like the imaginary part of the linear susceptibility, follow dynamic scaling with the critical exponents ? = 0.56(3) [? = 0.63(3)], ? = 1.80(5) [? = 2.0(1)], and z? = 10.1(1) [z? = 8.0(5)] in the sample with composition y = 0.2 (y = 0.3). The nonlinear susceptibility ?NL, which has contributions from both ?3 and ?5, satisfies static scaling with the same choice of Tg, ?, and ? . Irrespective of the Fe concentration, the values of the critical exponents ? , ?, and ? are in much better agreement with those theoretically predicted for a three-dimensional (d = 3) Heisenberg chiral SG than for a d = 3 Ising SG. The true thermodynamic nature of the ?zero-field? spin-glass transition is preserved even in finite magnetic fields. Unlike odd harmonics, even harmonics ?2(T,?) and ?4(T,?) make it evident that, apart from the macroscopic length scale of the spin-glass order in the static limit, there exists a length scale that corresponds to the short-range ferromagnetic order.

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