From Longman Dictionary of Contemporary Englishgive somebody the cold shouldergive somebody the cold shoulderinformalIGNORE to deliberately ignore someone or be unfriendly to them, especially because they have upset or offended you → cold
Examples from the Corpus
give somebody the cold shoulder• After I got the promotion, a few of my co-workers started giving me the cold shoulder.• So they have given girlfriends the cold shoulder.• She was sure that at some point she'd given some one the cold shoulder and hurt them badly without noticing.• Vernon regretted giving Harcourt the cold shoulder; he would have been some one to laugh with. 