2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/18757We solve a popular effective Hamiltonian of competing $d$-density wave and d-wave superconductivity orders self-consistently at the mean-field level for a wide range of doping and temperature. The theory predicts a temperature dependence of the $d$-density wave order parameter seemingly inconsistent with the neutron scattering and $μ$SR experiments of the cuprates. We further calculate thermodynamic quantities, such as chemical potential, entropy and specific heat. Their distinct features can be used to test the existence of the $d$-density wave order in cuprates.changed to 4 pages and 4 figures. More reference added. Accepted by Phys. Rev. BStrongly Correlated ElectronsSuperconductivitytext