will they break up? hostile neighbors

na

Id keep yourself in the chart, so you take Asc. Neighbors are Aquarius/Saturn whole sign 3rd. The lot of discord falls at 28° Saggitarius conjunct the Asc. Which both you and the neighbors retrograde back towards. So the bickering between them will not be ending anytime soon.

Now the SN is conjunct the lot too and in the first house, this makes the situation even more negative.

From this, it looks to be a continuing divisive situation between you and your neighbors. Which would mean that they will not be breaking up.

You're just going to have to disregard them the best you can.

I agree with Chrysalis that you are the ascendent, and your neighbour is the 3rd.
Mars and Neptune traditional divorce planets are sitting in the 3rd, showing not only the fights but an upcoming divorce. The husband and wife are mercury and Jupiter, and they do not make an aspect, mercury goes retrograde and will move away from Jupiter. In addition, moon will square Jupiter, confirming the separation. Moon is in your neighbour's 2nd house, approaching the square to his 12th house ruler, so money problems will probably force him to leave the apt. Chiron in his house also shows his situation, sufferance.
Your neighbour's wife, mercury, is in his 5th house of love affairs and children.
Moon just separates from a sextile with sun sitting on the cusp of his 5th, so it had been a happy event for him. Not sure which of these two might be the situation.

They are partners to all effects, a significant other, I would still consider them to be a relationship of 1st/7th, translated to the 3rd (and 7th from 3rd) as your neighbours.
However, if we do use the 5th (from the 3rd) for his partner, we still have mercury as her significator, which doesn't really change anything.