  The 1kHz real part $\chi'$ of the dielectric constant of a structural glass
was measured at low temperature $T$ down to 14 mK. Reducing the sample
thickness $h$ to 10 nm suppresses the usual minimum of $\chi'$ for measuring
fields $E<.5 $ MV/m. This contradicts the Two Level System (TLS) model but is
well accounted for by including TLS-TLS interactions where excitations
delocalize between TLS's through a $E$-induced mechanism recently designed: for
small $h$'s this interaction is reduced, which explains the two-dimensional
behavior of $\chi'(T)$. Hence, interactions play a key role in standard thick
samples.
