Specific heat and thermodynamic critical field for the molecular   metallic hydrogen
  In the framework of the Eliashberg formalism the free energy difference between the superconducting and normal state for the molecular metallic hydrogen was calculated. The pressure values $p_{1}=347$ GPa and $p_{2}=428$ GPa were taken into consideration. It has been shown, that together with the increase of the pressure, grows the value of the specific heat jump at the critical temperature and the value of the thermodynamic critical field near zero Kelvin: $[\Delta C(T_{C})]_{p2}/[\Delta C(T_{C})]_{p1}\simeq 2.33$ and $[H_{C}(0)]_{p2}/[H_{C}(0)]_{p1}\simeq 1.74$. Next, it has been stated, that the ratio $\Delta C(T_{C})/C^{N}(T_{C})$ also increases from 1.91 to 2.39; whereas $T_{C}C^{N}(T_{C})/H^{2}_{C}(0)$ decreases from 0.152 to 0.140. The last results prove that the considered parameters significantly diverge from the prediction based on the BCS model. 
R. Szczesniak, M.W. Jarosik
cond-mat.supr-con