It may be surprising that a Disney movie centered around two female characters, the sisters Elsa and Anna, could drive such staggering sales. But the real eye-opener is the strength and scope of the film’s grip on children, girls and boys alike. Parents are using words like “obsessed” and “cultlike” to describe the force with which the film is capturing little hearts and minds unlike any in recent memory.

“We have been doing so many ‘Frozen’ cakes, it’s crazy,” said Rachel Thebault, the owner of Tribeca Treats, a bakery in downtown Manhattan whose clients have included Jessica Biel and the New York Knicks star Carmelo Anthony. “In the seven years since we’ve been open, I have seriously not seen any other trend come close to this.”

With stores across the country sold out of the most coveted merchandise, desperate parents are turning to eBay, where, according to Bloomberg News, an original Elsa dress was recently offered for $1,600.

While brawling over the last must-have toy on the shelf is hardly unprecedented, “Frozen” is taking the madness to another level. A Manhattan mother said her son insists she call him Elsa while he runs around the house pretending to freeze everything. Another mother lamented that while her guests were around the table at Passover, her preschooler was in the other room singing, “Let It Go” at the top of his lungs.

Idina Menzel’s rendition of what has become the movie’s anthem, “Let it Go,” is a phenomenon unto itself, producing a level of passion and exuberance in children the likes of which some parents have never seen. I have been sent videos from friends who have captured the moment their children become possessed by the film’s song. One video featured Nora MacDonald, 3, of Sandwich, Mass., gently bouncing on a mini-trampoline in her gym class when “Let It Go” came over the speakers. Instantly infused with utter delight, she took off sprinting, almost flying, in ecstatic circles around the perimeter of the room.