Under what circumstances does the correlation between the long-term interest rate and inflation disappear?

The recent sharp rise in inflation in the United States and to a lesser degree in the euro zone has not led to a rise in long-term interest rates. We therefore examine: When the correlation between inflation and long-term interest rates has also disappeared in the past; What, when this is the case, the lack of correlation between long-term interest rates and inflation can be attributed to, in particular when it is inflation that rises: the absence of an acceleration in wages? Rise in inflation due only to commodity prices? The absence of a monetary policy response to the inflation? Underemployment? We find that: Decorrelations between rising inflation and rising long-term interest rates have previously occurred in the United States in 2005-2006, 2008 and 2011; and in the euro zone in 2008 and 2017-2018; Each time, it was due to some of the causes mentioned above (see breakdown in the conclusion); In 2021, the absence of both an acceleration in wages and a monetary policy response as well as underemployment have played a role.