On Stable Pair Potentials with an Attractive Tail, Remarks on Two Papers by A. G. Basuev

We revisit two old and apparently little known papers by Basuev (Teoret Mat Fiz 37(1):130–134, 1978 , Teoret Mat Fiz 39(1):94–105, 1979 ) and show that the results contained there yield strong improvements on current lower bounds of the convergence radius of the Mayer series for continuous particle systems interacting via a very large class of stable and tempered potentials, which includes the Lennard-Jones type potentials. In particular we analyze the case of the classical Lennard-Jones gas under the light of the Basuev scheme and, using also some new results (Yuhjtman in J Stat Phys 160(6): 1684–1695, 2015 ) on this model recently obtained by one of us, we provide a new lower bound for the Mayer series convergence radius of the classical Lennard-Jones gas, which improves by a factor of the order 10 5 on the current best lower bound recently obtained in de Lima and Procacci (J Stat Phys 157(3):422–435, 2014 ).