What is the ruling regarding a man telling his wife, "If you leave the house, you are divorced," with the intention of frightening and deterring her, not of divorce?

What you uttered is a conditional divorce of your wife upon her leaving the house. The majority of jurists hold that when the condition is met, the divorce occurs, whether the husband intended divorce or merely a threat. This is contrary to Ibn Taymiyyah, who does not consider the divorce to occur if the husband intended only a threat. What is preponderant in our view is the opinion of the majority. Therefore, if your wife leaves, the divorce has occurred, unless your prohibition was for a specific reason and that reason ceased without your intervention, in which case the divorce does not occur. We advise you to communicate with your wife with understanding and mutual respect, and to be cautious of uttering divorce.