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We present a theory for the spin-Peierls transition in CuGeO_3. We map theelementary excitations of the dimerized chain (solitons) on an effective Isingmodel. Inter-chain coupling (or phonons) then introduce a linear bindingpotential between a pair of soliton and anti-soliton, leading to a finitetransition temperature. We evaluate, as a function of temperature, the orderparameter, the singlet-triplet gap, the specific heat, and the susceptibilityand compare with experimental data on CuGeO_3. We find that CuGeO_3 is close toa first-order phase transition. We point out, that the famous scaling law\sim\delta^{2/3} of the triplet gap is a simple consequence of the linearbinding potential between pairs of solitons and anti-solitons in dimerized spinchains.Comment: 7.1 pages, figures include

physical review. b, condensed matter

Molecular-field approach to the spin-Peierls transition in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CuGeO</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Molecular-field approach to the spin-Peierls transition inCuGeO3