Both forms are correct. Arctic and artic are both correct spellings of two completely different nouns. When the first one is a geographic name, the second one is an informal abbreviation for articulated vehicle. They look similar in writing and also their pronunciations are a bit alike, consecutively /ˈɑːk.tɪk/ and / (ɑːˈtɪk) /, however they have completely different meanings and should not be confused.

Correct spelling, explanation: name of a geographic region.

Correct spelling, explanation: an informal abbreviation for articulated vehicle.

Definition of Artic:
noun: geographically; the large, very cold area around the North Pole;
The Arctic is always covered in snow, but there are animals that adapted to these conditions.
I would love to travel to the Arctic one day and see polar bears in their natural habitat.

Definition of artic:
noun: an abbreviation for an articulated vehicle; a large vehicle with a trailer, e.g a lorry;
To drive an artic you need to have an appropriate driving license.
I used to drive an artic for years, but last year I have moved to drive buses.