I don't talk to my husband for many reasons (he's unfaithful, he's absent all day since about 5 years and he strikes my 3 children and me...) for 4 months now. In fact, he hasn't talked to me since 4 months, and I also don't want to have any good thing with him. Is it Haram to continue not talking to each another? I think in Islam the man has to take care of the wife and I don't want to do anything for him even if he's my children's father.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Marital life should be based on love, affection and mutual confidence. Allah made a husband and wife source of tranquility to each other. Allah Says (interpretation of meaning): {… They are Lîbas [i.e. body cover, or screen, or Sakan, (i.e. you enjoy the pleasure of living with her), for you and you are the same for them. …} [2: 187].
He also Says: {And among His Signs is this, that He created for you wives from among yourselves, that you may find repose in them, and He has put between you affection and mercy. Verily, in that are indeed signs for a people who reflect.} [30: 21].
To achieve the love, affection and happiness both a husband and wife should fulfill the other's right, overlook the other's shortcomings and should advise each other kindly in good manners if he/she observes something wrong since every human being has shortcomings. Therefore, you should have not blamed your husband of unfaithfulness without legal evidence and you should not have left him due to his failure to fulfill your rights, or for beating you and your children.
We do not know the reason for his absence during the day. Is it for any legal reason in Shari'a or not? Therefore, we cannot give a ruling on this concern. Also, the reason for beating you or the children is not known to us.
However, our advice is that you should inform your father or any other Mahram to help solve the problem after discussing the reasons and circumstances in the way that pleases a spouse. Then you can have a happy conjugal life without having any separation, beating, blaming, disputes, etc.
We ask Allah to solve your problems.
Allah knows best.