Abrikosov parameter (${\beta }_A=⟨|\psi {|}^4⟩/⟨|\psi {|}^2{⟩}^2$)

A measure of spatial nonuniformity in the order parameter, with averages taken over one lattice cell. Set $X=|\psi {|}^2$. ThenEquality requires uniform $|\psi {|}^2$, so a nonconstant core pattern costs more in the quartic term than a uniform amplitude with the same mean squared amplitude. This identity alone does not compare two different vortex arrays: their admissible profiles must also satisfy the field equations.