Georgia Code Title 9. Civil Practice § 9-6-20

All official duties should be faithfully performed, and whenever, from any cause, a defect of legal justice would ensue from a failure to perform or from improper performance, the writ of mandamus may issue to compel a due performance if there is no other specific legal remedy for the legal rights; provided, however, that no writ of mandamus to compel the removal of a judge shall issue where no motion to recuse has been filed, if such motion is available, or where a motion to recuse has been denied after assignment to a separate judge for hearing.