FAILURE OF THE WKB APPROXIMATION IN CALCULATIONS OF SOLITON FREE-ENERGIES

The authors examine the accuracy of the WKB approximation used in previous work to compute soliton free energies at low temperatures; this examination is crucial in establishing the validity of a simple physical phenomenology as an alternative to the transfer-operator method of calculation. For the φ4 and double sine-Gordon potentials a method developed by Goldstein (1929) is adapted which is known to give correct results in the sine-Gordon case. For all three potentials, the WKB approximation is in error by the factor (eπ)12. © 1979 The American Physical Society.