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