Carter's "peace" was based on continuing aid to brutal regimes, meaning he was funding war even if not actively participating.
Carter's "peace," as you call it, was a period where not one bullet was fired, not one rocket launched by an American servicemen. That overseas funding you're talking about went into the realpolitik strategy of ensuring peace in other nations. Like it or not, democratic countries are more violent than their modern authoritarian counterparts. With Carter we had more peace than with any modern neoliberal.