Armie Hammer and Wife Elizabeth File for Divorce

Armie Hammer and his wife, Elizabeth Chambers have both just filed for divorce.

Elizabeth filed the divorce petition, and Armie filed his answer at the same time, so it was clearly coordinated.

There are differences. Elizabeth wants sole physical custody of their 2 children -- 5-year-old Harper Grace and 3-year-old Ford. Armie is asking for joint legal and physical custody.

Elizabeth cites the usual -- irreconcilable differences -- as the reason for the divorce.

Sources connected to the couple tell TMZ ... there is NO PRENUP. Based on the documents it appears Armie will pay spousal and child support. The date of separation is interesting ... Armie lists January and Elizabeth lists July. This is a crucial difference ... if the judge accepts her version, they would have been together as a married couple for just over 10 years, and that could affect spousal support. If January is the date, it's under 10 years.

Armie said earlier today ... "Thirteen years as best friends, soulmates, partners and then parents. It has been an incredible journey, but together, we’ve decided to turn the page and move on from our marriage."

He adds ... "As we enter into this next chapter, our children and relationship as co parents and dear friends will remain our priority."

His Instagram post concludes with, "We understand this news lends itself to public dialogue, but in the interest of our children and our family, we’re asking for privacy, compassion and love during this time."  Elizabeth shared the same IG post at the same time as Armie.

At the end of May, Elizabeth posted this -- "TEN years married, twelve together, thirteen years as best friends. Happy Anniversary, my love. I’m beyond grateful for you, this decade, our family and the dreamiest Friday night anniversary sunset." Notice the all caps on "TEN" ... sure seems like she wanted to emphasize, in her eyes, they'd reached that crucial mark.

Armie, Elizabeth and their kids have been quarantining together in the Cayman Islands ... where Armie spent some of his childhood.

It's the first marriage for both Armie and Elizabeth.

Armie is repped by disso queen Laura Wasser, and Elizabeth is repped by Kristina Royce.