  We have performed a detailed analysis of the X-ray spectra of the blazar Mkn
421 using Swift-XRT observations taken between 2005 and 2020, to quantify the
correlations between spectral parameters for different models. In an earlier
work, it has been shown that such spectral parameter correlations obtained from
a single short flare of duration $\sim$ 5-days of Mkn 421, can be used to
distinguish spectrally degenerate models and provide estimates of physical
quantities. In this work, we show that the results from the long-term spectral
parameter correlations are consistent with those obtained from the single
flare. In particular, that the observed spectral curvature is due to maximum
cutoff energy in the particle distribution is ruled out. Instead, models where
the curvature is due to the energy dependence of escape or acceleration
time-scale of the particles are favored. The estimated values of the physical
parameters for these models are similar to the ones obtained from the single
flare analysis and are somewhat incompatible with the physical assumption of
the models, suggesting that more complex physical models are required. The
consistency of the results obtained from the long and short-term evolution of
the source, underlines the reliability of the technique to use spectral
parameter correlations to distinguish physical models.
