Her husband frequently swears by divorce. Is she still married to him?

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Check below answers in case you are looking for other related questions:
He swore to divorce her if she visited her family, and now he has recanted. Does he have to offer kafaarat yameen?
Divorce uttered in anger

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Related Answers:
Does the Throne of Allaah shake because of divorce?
Implicit divorce in the event of doubt concerning the intention or when there is waswasah
He divorced his wife, and her ‘iddah has finished, can he remarry her without returning to the court?
He swore to divorce her if she visited her family, and now he has recanted. Does he have to offer kafaarat yameen?
Divorce uttered in anger

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