High-quality KFe2As2 (K122) single crystals synthesized by different techniques have been studied by magnetization and specific heat (SH) measurements. There are 2 types of samples both affected by disordered magnetic phases: (i) cluster-glass (CG) like or (ii) Griffiths phase (G) like. For (i) at low applied magnetic fields the T-dependence of the zero field cooled (ZFC) linear susceptibility (chi_l) exhibits an anomaly with an irreversible behavior in ZFC and field cooled (FC) data. This anomaly is related to the freezing temperature T_f. The extrapolated T_f to B=0 varies between 50 K and 90 K. Below T_f we observed a magnetic hysteresis in the field dependence of the isothermal magnetization (M(B)). The frequency shift of the freezing temperature delta T_f=Delta T_f/[T_fDelta(ln u)]sim 0.05$ has an intermediate value, which provides evidence for the formation of a CG-like state in the K122 samples of type (i). The frequency dependence of their T_f follows a conventional power-law divergence of critical slowing down: tau=tau_0 [T_f(nu)/T_f(0)-1]^{-z u^{}} with the critical exponent z u^{}=10(2) and a relatively long characteristic time constant tau_0 =6.9 x10^{-11}$s also supporting a CG behavior. The large value of the Sommerfeld coefficient was related to magnetic contribution from a CG. Samples from (ii) did not show a hysteresis behavior for chi_l(T) and M(B). Below a crossover temperature T^* sim 40 K a power-law dependence in the chi_l propto T^[lambda_G-1}], with a non-universal lambda_G was observed, suggesting a quantum G-like behavior. In this case chi_l and M(B) can be scaled using the scaling function M_s(T,B)= B^{1-lambda_{tiny G}}Y(mu B/k_BT) with the scaling moment mu of the order of 3.5mu_b. The same non-universal exponent was found also in SH measurements, where the magnetic contribution C/T propto T^(lambda_G-1).
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