We study the critical points of a nonlocal free energy functional. The functional has two minimizers (ground states) m(±)m(±) with zero energy. We prove that there is a first excited state identified as the instanton m̂ Lm̂L, and that above the energy of the instanton there is a gap. We also characterize parts of the basin of attraction of m(±)m(±) and m̂ Lm̂L under a dynamics associated to the free energy functional. The result completes the analysis of tunneling from m(−)m(−) to m(+)m(+)
