Dimensionless quantities of hysteresis loops

•A method of dimensionless quantities for the analysis of hysteresis phenomena.•Dimensionless hysteresis quantities of zero, first, second and third orders.•Analytic expressions for dimensionless hysteresis quantities in a weak magnetic field.•Scaling in the Rayleigh region extends over the entire region of the magnetic field in which permeability increases.•Analytical expressions for hysteresis losses and permeability. A method of dimensionless quantities for the analysis of hysteresis phenomena is proposed. Dimensionless hysteresis quantities of zero, first, second and third orders are introduced. Analytic expressions are obtained for dimensionless hysteresis quantities in a weak magnetic field. In the Rayleigh region, the order of dimensionless hysteresis quantities coincides with the exponent of the power function that relates these quantities with a hysteresis factor κr. It is shown that the scaling in the Rayleigh region extends over the entire region of the magnetic field in which permeability increases. Analytical expressions for the hysteresis losses and permeability are obtained, which are confirmed experimentally.