Is it correct to call java.lang.String immutable?

This Java tutorial says that an immutable object cannot change its state after creation.

java.lang.String has a field

/** Cache the hash code for the string */
private int hash; // Default to 0

which is initialized on the first call of the hashCode() method, so it changes after creation:

    String s = new String(new char[] {' '});
    Field hash = s.getClass().getDeclaredField("hash");
    hash.setAccessible(true);
    System.out.println(hash.get(s));
    s.hashCode();
    System.out.println(hash.get(s));

output

0
32

Is it correct to call String immutable?