Step 1: Recall the code requirement.
According to IS 456:2000, the diameter of lateral ties in a reinforced concrete column shall not be less than
\[
6\,\mathrm{mm}.
\]
Step 2: State the correct answer.
Therefore,
\[
\boxed{6\,\mathrm{mm}}
\]
is the minimum permitted diameter.
Hence,
\[
\boxed{(C)}
\]
is the correct answer.