Hello Olive, It is rather "Things are going south". Don't use the preposition 'to' here. 'to go south' is an idiomatic expression. It could be used in oral as well as in written English. When things are going south ,it means they are loosing value or quality. It could also mean to stop working. Examples: The market went south, which caused problems right across the economy. ( The market values declined etc...) Olive was on a business trip to New York when his laptop computer went south. ( It stopped working)

Hi Olive, Things go south" usually means "things go bad." "Accusing someone of lying will usually cause things to go south pretty fast," would mean that things/the situation/the relationship will go bad very quickly.