NEW YORK — A city Health Department study finds that more than a fourth of adult New Yorkers are infected with the virus that causes genital herpes. The study, released Monday, says about 26 percent of New York City adults have genital herpes, compared to about 19 percent nationwide. The department says genital herpes can double a person’s risk for contracting HIV. Herpes can cause painful sores, but most people have no recognizable symptoms. Among New Yorkers, the herpes rate is higher among women, black people and gay men. The health department urges consistent use of condoms, and says its STD clinics offer free, confidential herpes testing.