And then you told your landlord. And then the refrigerator was replaced by you, with your landlord agreeing to pick up the tab via a deduction from your rent.

Other than by failing to anticipate that the refrigerator would break in a most unusual way, driving up your electric bill, what is it that you believe your landlord did wrong? I'm not saying that the outcome is fair, mind you, but if your landlord acted (or authorized you to act) as soon as the problem was reported, what duty do you believe was violated?