Confinement and Critical Regime in Doped Frustrated Quasi-One Dimensional Magnets

Ground state and finite temperature properties of a system of coupledfrustrated and/or dimerized spin-1/2 chains modeling e.g. the CuGeO$_3$compound are reviewed. Special emphasis is put on the investigation of the roleof impurity doping. A c hain-mean field computation combining exactdiagonalisations of the chain hamiltonians together with a mean field treatmentof the weak interchain couplings is performed in order to map the microscopicmodel onto a low-energy effective model. The latter descr ibes a 2-dimensionalsystem of effective spin-1/2 local moments interacting by spacially anisotropiclong range spin exchange interactions. An extensive study of this effectivemodel is performed by Stocastic Series Expansion Quantum Monte Carlo for a widerange of temperatures and impurity concentrations. Interesting scalingbehaviors of the uniform and staggered spin susceptibilities (above a smallordering Neel temperature due to a residual 3D coupling) can be interpreted interms of the formation of large clusters of correlated spins carrying a finitemagnetization. Such results are reproduced satisfactorily by a new Real SpaceRG enabling to deal with long range interactions in two-dimensionsComment: Invited paper at SPQS, Sendai July 2004. 8 pages + 15 figure