Display posts from a specific category on frontpage.php template?

Take a look at multiple loops for examples

And also look at the content.php file in the Twenty Fourteen theme

<?php

// The Query
$category_query = new WP_Query( 'category__in=11' );

// The Loop
if ( $category_query->have_posts() ) {
    echo '<ul>';
    while ( $category_query->have_posts() ) {
        $category_query->the_post();
        echo '<li>' . get_the_title() . '</li>';
    }
    echo '</ul>';
} else {

}
/* Restore original Post Data */
wp_reset_postdata();

Don’t forget you can use pre_get_posts to alter an existing loop and exclude categories from any loop.