Abstract
We study the discreteness effects on kink static properties in a one-dimensional anharmonic ${\mathrm{\ensuremath{\Phi}}}^{4}$ chain with a long-range interaction potential of Kac-Baker type. Using the Dirac's second class constraints, we show that the discrete kink experiences the periodic Peierls-Nabarro (PN) potential whose barrier depends strongly on the range of interaction. Numerical calculations reveal that the dressing of the kink profile by the lattice effects lowers the PN potential and considerably increases its barrier. It is seen that the dressing and its effects tend to disappear when the range of interaction increases.
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