Number of metastable states of a chain with competing and anharmonicΦ4−like interactions

We investigate the number of metastable configurations of a ${\mathrm{\Phi }}^4$-like model with competing and anharmonic interactions as a function of an effective coupling constant η. The model has piecewise harmonic nearest-neighbor and harmonic next-nearerst-neighbor interactions. The number M of metastable states in the configuration space increases exponentially with the number N of particles: M∝exp(νN). It is shown numerically that, outside the previously considered range ‖η‖<1/3, ν is approximately linearly decreasing with η for ‖η‖<1 and that ν=0 for η≥1. These findings can be understood by describing the metastable configurations as an arrangement of kink solitons whose width increases with η.