On the Lattice Corrections to the Free Energy of Kink-Bearing Nonlinear One-Dimensional Scalar Systems
D. Grecu, Anca Visinescu (Department of Theoretical Physics, Institute, of Atomic Physics, P.O.Box MG-6,Magurele,Bucharest,Romania)
TL;DR
This paper provides a rigorous proof and detailed calculation of lattice corrections to the free energy in nonlinear one-dimensional scalar systems with kinks, confirming previous first-order energy estimates.
Contribution
It offers a rigorous proof of the effective potential with lattice corrections and computes these corrections using asymptotic methods, aligning with earlier energy estimates.
Findings
Lattice corrections to kink free energy are explicitly calculated.
Results agree with first-order static kink energy corrections.
Provides a rigorous mathematical foundation for previous heuristic results.
Abstract
A ri proof of the effective potential (lattice corrections included) deduced by Trullinger and Sasaki is given. Using asymptotic methods from the theory of differential equations depending on a large parameter, the lattice corrections to the kink and kink-kink contributions to the free energy are calculated. The results are in complete agreement with a first order correction to the energy of the static kink.
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