The present behaviour of the geomagnetic field as expressed by the International Geomagnetic Reference Field (IGRF) deserves special attention when compared with that shown over the past few thousands of years by two paleomagnetic/archeomagnetic models, CALS3K and CALS7K. The application of the Information theory in terms of Shannon Information and K-entropy to these models shows characteristics of an instable geomagnetic field. Although the result is mitigated when we correct the CALS7K model

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... or its typical spectral damping, the present geomagnetic field as represented by IGRF is still rather distinct, at least for the past 4000 years, a result that is further confirmed by the CALS3K model. This is consistent with a significant global critical state started at around 1750, and still present, characterised by significant decays of the geomagnetic dipole, energy and Shannon information and high K-entropy. The details of how these characteristics may develop are not clear, since the present state could move toward an excursion or a geomagnetic polarity reversal, but we cannot exclude the possibility that the "critical" behaviour will become again more "normal", stopping the apparent trend of the recent geomagnetic field decay.