Warranty of habitability
A promise built into New Jersey residential leases, written or not, that the landlord will keep your home safe, sanitary, and fit to live in, with basics like heat, water, and working plumbing.
New Jersey example
Your Elizabeth apartment has had no heat for a week in January. The DCA guide says to tell the landlord in writing by certified mail, return receipt requested, and give them reasonable time to fix it. If they don't, the guide lists options like asking a court for a rent reduction, but any rent you withhold should be saved in case a judge orders you to pay it.
Official source
This is a plain-English summary. Rules and dollar amounts change, so check the official source or a professional before you file or sign anything.