  Studies of low-frequency resistance noise show that the glassy freezing of
the two-dimensional electron system (2DES) in Si in the vicinity of the
metal-insulator transition (MIT) persists in parallel magnetic fields B of up
to 9 T. At low B, both the glass transition density $n_g$ and $n_c$, the
critical density for the MIT, increase with B such that the width of the
metallic glass phase ($n_c<n_s<n_g$) increases with B. At higher B, where the
2DES is spin polarized, $n_c$ and $n_g$ no longer depend on B. Our results
demonstrate that charge, as opposed to spin, degrees of freedom are responsible
for glassy ordering of the 2DES near the MIT.
