Molecular-field approach to the spin-Peierls transition in CuGeO_3

We present a theory for the spin-Peierls transition in CuGeO_3. We map the elementary excitations of the dimerized chain (solitons) on an effective Ising model. Inter-chain coupling (or phonons) then introduce a linear binding potential between a pair of soliton and anti-soliton, leading to a finite transition temperature. We evaluate, as a function of temperature, the order parameter, the singlet-triplet gap, the specific heat, and the susceptibility and compare with experimental data on CuGeO_3. We find that CuGeO_3 is close to a 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 linear binding potential between pairs of solitons and anti-solitons in dimerized spin chains.