Thermodynamic properties of the d-density wave order in cuprates

We 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 $\mu$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.