Limits to magnetic quantum criticality from nuclear spins

The phenomenology of quantum phase transitions concerns physics at low temperatures and energies, corresponding solid-state experiments often reach millikelvin temperatures. However, this is a scale where in many solids the influence nuclear spins their hyperfine interaction no longer negligible. This may limit observability electronic critical phenomena. Here we discuss how continuous magnetic get influenced, modified, or destroyed by coupling to spins. We use simple yet paradigmatic spin models for criticality determine modifications diagram, excitation spectrum, thermodynamics due presence estimate crossover scales below which purely observable, novel emerging Our results are relevant variety compounds displaying and, more generally, highlight sensitivity systems small perturbations.