Jump quantum phase transitions in a vortex sistem and the dinamic complex magnetic permeability of high-temperature binary YBa$_2$Cu$_3$O$_{7-x}$ superconductors

A nonlocal high-frequency method for measuring the dynamic complex magnetic permeability with enhanced spatial resolution is developed to simultaneously determine the bulk and local character of stepwise penetration of a magnetic flux through twin boundaries (TBs) into a YBa$_2$Cu$_3$O$_{7-x}$ HTSC sample during its stepwise decomposition into twins. By the values of fields corresponding to the regions of steps, the thermodynamic first critical magnetic fields are determined: the penetration of a flux into a sample – a Josephson medium; the development of a critical state in the Josephson medium; the penetration of a flux into twins; and the values of the critical fields of phase transitions in the vortex system of the HTSC sample, such as the melting fields of a vortex crystal, the formation of a superconducting glass state in the sample, and the transition to the vortex glass and Bragg glass states.