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In this paper, we investigate an approximate technique for the calculation of the free energy of fermionic systems that are coupled to topological solitons. We apply this to a solvable onedimensional model field theory: plyacetylene in the static dimerization approximation. We estimate the free energy of solitons with various scales of spatial exten. sion and make comparisons with exact results. In an appendix. we make the connection between the high-temperature limit of our work anddoi:10.1088/0953-8984/3/35/006 fatcat:gphzc2ygrrdl5mx3arjxuacksy