This work is aimed at investigating the presence of diffuse radio emission in low-mass (M_ 500 łeq3 M_⊙) relaxed galaxy clusters. 14 We present a pilot study for the MIMIC (MIni-halos in MIni-Clusters) project, focusing on Abell 496 and ZwCl 235, using LOFAR (54 MHz, 144 MHz), uGMRT (400 MHz, 650 MHz), and MeerKAT (1.28 GHz) data, as well as X-ray data. Chandra We detected diffuse radio emission in the central ∼100 kpc of both Abell 496 and ZwCl 235, spatially confined within the sloshing-induced cold fronts seen in X-ray images. The diffuse sources satisfy the classification criteria for radio mini-halos and represent the least powerful known to date, with 1.4 GHz radio powers of (2.2 W/Hz in Abell 496 and (1.3 W/Hz in ZwCl 235. The mini-halos have steep spectra (-1.9łeq In particular, in Abell 496, we find an outward steepening of the spectral index. In both clusters, the radio and X-ray surface brightness are correlated over the diffuse source extent, with sublinear or nearly linear slopes depending on frequency. Separately, we present the properties of two extended ($>200$ kpc) tailed radio galaxies in both clusters. The steep spectra, sublinear radio–X-ray correlations, and confinement within cold fronts suggest that contribution from fossil plasma advected from the central radio galaxy and plausible turbulent reacceleration are at play in Abell 496 and ZwCl 235. These two systems allow us to extend mini-halo scaling relations toward the low-power regime. We confirm a strong correlation between the mini-halo radio power and the cool core X-ray luminosity, with P_ 1.4 ∝ L_ X,70 ^ 1.5 . We find, for the first time, tentative indications that mini-halos with steeper radio spectra could preferentially be associated with lower core X-ray luminosities and lower radio power. We speculate that mini-halos may originate from a combination of hadronic and leptonic reacceleration mechanisms, whose relative importance varies with the properties of the host cluster: higher core X-ray luminosities at a given mass (i.e., reflecting higher gas densities) might make the contribution of hadronic interactions more substantial.
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