Phase transitions in a MgB$_{2}$ granular BCS superconductor in weak magnetic fields

The character of temperature dependences of the electric conductivity of MgB$_{2}$ granular BCS superconductors at temperatures of $\sim$35–45 K in external magnetic fields H ext of up to $\sim$2 kOe is studied. An increase in the superconducting transition width $\Delta T_{c}$ with an increase in Hext is found. The presence of a system of weak links in MgB$_{2}$-based granular superconductors is established. On the basis of experimental data, MgB$_{2}$ granular superconductor is assigned to two-level superconducting systems and the $H$–$T$ phase diagram is constructed.