Link to single.php and single_x.php

How can I change this Link:

<a href="<?php the_permalink() ?>"><?php the_title(); ?></a>

to link to page single_x.php instead of to single.php?

I want to change that link in my archiv.php to link to a different design:

Let’s say home.php links to single.php
and archive.php links to single_x.php

King regards,
Felix