archive.php is not used for subsequent pages of non-search, non-taxonomy, ... based subsets of content.
I think you might be looking for paged.php (but that'll also be used for the first page).
Alternatively add logic to index.php to call a different template where page number is greater than one.
Correction on reviewing http://codex.wordpress.org/Template_Hierarchy#Visual_Overview pages.php is not the answer. Paged (ie. not single) posts use home.php otherwise index.php only.
So you'll need to put in your own logic (presumably to home.php) to use index.php or some custom template for posts.
(This answer shows the WP logic to decide which template to use.)