My wife not responding to my request for contact since Nikah. Could you please tell me whether it is permissible for a husband to beat his wife?

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

If what you mentioned about this lady is authentic, then she is Nasheez who does not obey her husband. So, she must repent to Allah and should know that she is confronted by the Anger of Allah as long as she has not repented al-Bukhari and Muslim reported: "If a woman spends her night leaving the bed of her husband the angels will curse her till morning".
Her husband should first advise her. If that does not help, then he should stop having sex with her. If all this does not bring a solution, then he can beat her but in a civilized manner. If she still refuses to go back to wedded life, then he can take the case to the Qadi or the one who represents him or even Islamic centers that can serve as judges between them.
Allah Says (interpretation of meaning): {… As to those women on whose part you see illconduct, admonish them (first), (next), refuse to share their beds, (and last) beat them (lightly, if it is useful), but if they return to obedience, seek not against them means (of annoyance). Surely, Allâh is Ever Most High, Most Great. If you fear a breach between them twain (the man and his wife), appoint (two) arbitrators, one from his family and the other from her's; if they both wish for peace, Allâh will cause their reconciliation. Indeed Allâh is Ever All Knower, Well Acquainted with all things.}[4: 34-35].
Anyway, divorce is in the hand of the man and it is lawful for him to do it under all circumstances as long as the woman is not menstruating or in a period of purity where he has had sex with her.
So, if the habitual ways of reconciliation do not have any effect, then divorce is the last resort, the last solution.
Allah knows best.