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We report extensive muon spin rotation measurements on the lightly dopedY1-xCaxBa2Cu3O6+y compound, which allows us to disentangle the effect ofdisorder, controlled by random Ca2+ substitution, from that of mere doping. A3D phase diagram of lightly doped cuprates is accurately drawn, showing that athermally activated antiferromagnetic phase competes with superconductivityaround a quantum critical point, hidden underneath a frozen insulating magneticstate. Disorder suppresses both competing order parameters and unveils theunderlying frozen state. Doping and disorder destroy the activated magneticphase along a line of first order phase transitions that ends at the criticalpoint.

Competing orders suppressed by disorder around a hidden quantum critical point in cuprate high Tc superconductors