This is a good article which outlines Social Security benefits for divorced people. The article refers to "divorced women", but it also applies to divorced men (especially if the woman had higher earnings).
Excerpt :
The law says a divorced woman, who was married to her ex-husband for a minimum of 10 years, is due essentially the same benefits as a woman who is currently married to her husband.
In a nutshell, that means a divorced woman can get between one-third and one-half of her ex-husband’s Social Security (depending on her age) while he is alive and between 70 percent and 100 percent of his Social Security (depending on her age) after he dies.