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We accurately treat the effect of the double and triple interactions oftwo-level systems (TLS) in glasses onto the energy delocalization due to thelong-range interaction of TLS. Although this work qualitatively reproduces theestimates of our previous work we believe that it is important because in thispaper the estimates are done with quantitative accuracy. This work can serve asthe important step towards the development of quantitative theory of many-bodydelocalization due to the long-range interaction. Our study is compared withthe recent work by Bodea et al claiming that the interaction of TLS triplesleads to the energy delocalization. We cannot agree with the mentioned workbecause as we show the interaction of TLS triples was overestimated there andtherefore the result for the TLS relaxation rate obtained there is invalid.

Effect of triple interaction on energy delocalization in the strongly disordered system of interacting two-level defects