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I often hear that in a superfluid, vortices get arranged in a lattice but I don't understand why and I've been hard pressed to find a discussion of it online.
I'm aware that vortices should repel due to the magnus force between them, but should n't there also be some long range attraction to balance the repulsion to create a lattice? Or does the lattice only appear at high vortex density?
You are correct that vortices in e.g. a type II superconductor will repel each other. Since they are stuck in the superconducting material, they will form a lattice when trying to maximize the distance between each other. The higher the density of the vortices will be, the more they will be able to form a densely packed and static lattice. You can find a discussion of vortices, how they form a lattice and their corresponding physics in these lecture notes by Christopher Henley.
