Using the auto-entered text calculation should work for you provided that the record is not comitted in between editing data into field_two. If that's a possibility, then an On ObjectValidate, OnObjectSave or OnObjectExit script trigger could be used to check for a matching duplicate value.
Define a self-join relationship:
YourTable::Field1 = YourTable 2::Field1 AND
YourTable::Field2 = YourTable 2::Field2
Where YourTable 2 is a new table occurrence of YourTable. (Select YourTable, then click button with two gree plus signs to make this new table occurrence.)
Your script can then use count ( YourTable 2::Field1 ) to see if a duplicate records exists. (The count will be greater than 1 if a duplicate exists.)