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Oh, I was speaking in general, but that size is just right for Myrmica.

Do they both seem roughly the same size? They look like Myrmica to me. 1cm would be a little under twice their actual size, by the way.

Myrmica queens are small, about the size of a Formica worker. Try to get measurements in mm, if you can.

Way too late for Tetramorium to be flying.
Let's get some pictures!

Nice haul! The queen(s) in the first two images are Pogonomyrmex rugosus . The third image is also Pogonomyrmex , but is she a different color? or is the lighting weird? Images four through six look like the dark variant of Solenopsis xyloni . And the remainder are Solenopsis xyloni or Solenopsis in...

That doesn't look like a bad spot, but it generally takes time to get a good feel for where to find ants. As you look next summer, you will no doubt find areas where you see many queens, and areas where you find few. The season isn't over yet, so keep looking on warm, humid days.

Take your pictures now, so you can figure out what kind of care they need. Not all queens found colonies the same way.

Searching in parks and paths along the edges of forests are the best, in my experience. During mating flights, queens will theoretically be dispersed everywhere, so there is a balance of finding areas with lots of ants and looking in places where they will be easily visible to you.

Mikey's Solenopsis colony experiences tropical temperatures year-round, so a Solenopsis invicta in Tennessee will probably be somewhat manageable.

Lasius neoniger