Electronic nematicity in correlated metals often occurs alongside another instability such as magnetism. As a result, the question remains whether nematicity alone can drive unconventional superconductivity or anomalous (quantum critical) transport in such systems. In FeSe, nematicity emerges in isolation, providing a unique opportunity to address this question. Studies to date, however, have proved inconclusive; while signatures of nematic criticality are observed upon sulfur substitution, they appear to be quenched under the application of pressure due to the emergent magnetism. Here, we study the temperature and pressure dependence of the low-temperature resistivity of FeSe$_{1-x}$S$_{x}$ crystals at $x$ values just beyond the nematic quantum critical point. Two distinct components to the resistivity are revealed; one whose magnitude falls with increasing pressure and one which grows upon approaching the magnetic state at higher pressures. These findings indicate that nematic and magnetic critical fluctuations in FeSe$_{1-x}$S$_{x}$ are completely decoupled, in marked contrast to other Fe-based superconductors, and that nematic fluctuations alone may be responsible for the transport signatures of quantum criticality found in FeSe$_{1-x}$S$_{x}$ at ambient pressure.
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