Combine the lime juice and sugar in a bowl and whisk to dissolve the sugar. Pour half of this mixture into an electric blender, add 1 cup vodka and 4 cups ice and blend until smooth. Divide among 4 glasses, such as margarita glasses or other wide-mouthed, stemmed glasses. Repeat with the remaining ingredients. Serve immediately with lime slices for garnish.
Makes 8 servings