Put an end to potential arguments as quickly as possible.
Sometimes students having an argument may not be breaking a specific rule of the class. This is why teachers would be wise to have a catch all rule that says something like “no uncivilized behavior allowed.” When this rule is in place, consequences can reasonably be given for unexpected misbehaviors.
If an argument goes too far, the best plan is to remove the students involved from the room quickly. Even if this means just taking them into the hallway for a private discussion, this can be an effective way to diffuse the situation. The best solution, of course, is to try to end the disagreement before it gets to that point.