  Primordial magnetic fields (PMFs) are possible candidates for explaining the
observed magnetic fields in galaxy clusters. Two competing scenarios of
primordial magnetogenesis have been discussed in the literature: inflationary
and phase-transitional. We study the amplification of both large- and
small-scale correlated magnetic fields, corresponding to inflation- and phase
transition-generated PMFs, in a massive galaxy cluster. We employ
high-resolution magnetohydrodynamic cosmological zoom-in simulations to resolve
the turbulent motions in the intracluster medium. We find that the turbulent
amplification is more efficient for the large-scale inflationary models, while
the phase transition-generated seed fields show moderate growth. The
differences between the models are imprinted on the spectral characteristics of
the field (such as the amplitude and the shape of the magnetic power spectrum)
and therefore on the final correlation length. We find a one order of magnitude
difference between the final strengths of the inflation- and phase
transition-generated magnetic fields, and a factor of 1.5 difference between
their final coherence scales. Thus, the final configuration of the magnetic
field retains information about the PMF generation scenarios. Our findings have
implications for future extragalactic Faraday rotation surveys with the
possibility of distinguishing between different magnetogenesis scenarios.
