the localized particles have Skyrmionic character.

We organize this paper as follows. In Sec. II we summarize our implementation of finite-size HF theory in the lowest Landau level (LLL). In Sec. III and IV we present and discuss our numerical results for calculations at $\nu=1$ and $\nu\ne 1$. The possibility, discussed in recent work,[@Nederveen] that at $\nu=1$ disorder will induce reduced-size Skyrmion-anti-Skyrmion pairs in the ground state is specifically addressed in Sec. III. Finally, in Sec. V we present our conclusions.

Hartree-Fock Theory in the LLL
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The HF approximation allows the interplay between disorder and interactions to be addressed while retaining a simple independent-particle picture of the many-body ground state. For the current study, the use of this approximation is underpinned by the fact that it reproduces the exact ground state at $\nu=1$ in both weak interaction and strong interaction[@general] limits. HF theory is a self-consistent mean field theory, and as such it has strengths and shortcomings, which we discuss later. In this section, we outline the basic formalism of HF approximation calculations in the LLL limit.

In a strong magnetic field, the Landau level splitting is very large and, since excitations to higher Landau levels are effectively forbidden 