Are judges considered 'public figures' under common law?

and can they legally sue a newspaper for libelous statements?
In terms of the law of defamation and its interaction with free speech, yes, judges are public figures. ANYONE can sue a paper for libelous statements, public or private people alike.
Yes and 'sort of'.

They can sue, but they have to prove malicious intent, and they have to prove that the newspaper knew the statement that they were making was false.


Answer:
We'd need more facts to answer, truthfully, because there are so many different types of judges. Most will be at least limited-purpose public figures.

Assuming some form of public-figure identity, a lawsuit from a judge would have to show 'actual malice,' which is either intentional falsity or reckless disregard for the truth and falsity of a statement.

The reason is that the United States does not stand in the way of criticism of public officials. Citizens have the right to criticize the government, so the higher 'actual malice' standard must be proven.