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We argue that there is a special doping point in the phase diagram ofcuprates, such that the condensation of holes into a charge-ordered and into asuperconducting phase are degenerate in energy but with an energy barrier inbetween. We present a Monte Carlo simulation of this problem without and withquenched disorder. While in the clean case charge order and superconductivityare separated by a first-order line which is nearly independent of temperature,in the presence of quenched disorder, charge order is fragmented into domainsseparated by superconducting filaments reminiscent of the supersolid behaviorin $^4$He. The resulting phase diagram is in good agreement with theexperiments.

Thermodynamic phase diagram of the competition between superconductivity and charge order in cuprates