  Potts glasses are prototype models that have been used to understand the
structural glass transition. However, in finite space dimensions a glass
transition remains to be detected in the 10-state Potts glass. Using a
one-dimensional model with long-range power-law interactions we present
evidence that a glass transition below the upper critical dimension can exist
for short-range systems at low enough temperatures. Gaining insights into the
structural glass transition for short-range systems using spin models is thus
potentially possible, yet difficult.
