Does a divorce occur with the statement, "There are many men other than me, and you can renew your life," accompanied by the intention of divorce, given that the speaker believed that divorce does not occur except with an explicit verbalization?

Your agreement with your wife to separate after a period is merely a promise and is not considered a divorce. And your statements to your wife, such as, "There are many other men besides me, and you can renew your life," and similar phrases, are allusive expressions that could imply divorce or something else. A divorce does not occur through them unless you intend to effect it. Accordingly, as long as you did not intend to effect a divorce with these phrases, no divorce has occurred, and your wife is still under your marital bond.