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We report on 13 new high-precision measurements of stellar diameters forlow-mass dwarfs obtained by means of near-infrared long-baseline interferometrywith PIONIER at the Very Large Telescope Interferometer. Together with accurateparallaxes from Gaia DR2, these measurements provide precise estimates fortheir linear radii, effective temperatures, masses, and luminosities. Thisallows us to refine the effective temperature scale, in particular towards thecoolest M-dwarfs. We measure for late-type stars with enhanced metallicityslightly inflated radii, whereas for stars with decreased metallicity wemeasure smaller radii. We further show that Gaia DR2 effective temperatures forM-dwarfs are underestimated by $\sim$ 8.2 % and give an empirical$M_{G}$-$T_{\rm eff}$ relation which is better suited for M-dwarfs with $T_{\rmeff}$ between 2600 and 4000 K. Most importantly, we are able to observationallyidentify a discontinuity in the $T_{\rm eff}$-radius plane, which is likely dueto the transition from partially convective M-dwarfs to the fully convectiveregime. We found this transition to happen between 3200 K and 3340 K, orequivalently for stars with masses $\approx 0.23 M_{\odot}$. We find that inthis transition region the stellar radii are in the range from 0.18 to0.42$R_{\odot}$ for similar stellar effective temperatures.

A discontinuity in the $T_{\rm eff}$-radius relation of M-dwarfs