3 research outputs found

    On the Application of the Non Linear Sigma Model to Spin Chains and Spin Ladders

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    We review the non linear sigma model approach (NLSM) to spin chains and spin ladders, presenting new results. The generalization of the Haldane's map to ladders in the Hamiltonian approach, give rise to different values of the θ\theta parameter depending on the spin S, the number of legs nℓn_{\ell} and the choice of blocks needed to built up the NLSM fields. For rectangular blocks we obtain θ=0\theta = 0 or 2πS2 \pi S depending on wether nℓn_{\ell}, is even or odd, while for diagonal blocks we obtain θ=2πSnℓ\theta = 2 \pi S n_{\ell}. Both results agree modulo 2π2 \pi, and yield the same prediction, namely that even ( resp. odd) ladders are gapped (resp. gapless). For even legged ladders we show that the spin gap collapses exponentially with nℓn_{\ell} and we propose a finite size correction to the gap formula recently derived by Chakravarty using the 2+1 NSLM, which gives a good fit of numerical results. We show the existence of a Haldane phase in the two legged ladder using diagonal blocks and finally we consider the phase diagram of dimerized ladders.Comment: 25 pages, Latex, 7 figures in postscript files, Proc. of the 1996 El Escorial Summer School on "Strongly Correlated Magnetic and Superconducting Systems". Some more references are adde

    GEL ENTRAPMENT AND MICRO-ENCAPSULATION: METHODS, APPLICATIONS AND ENGINEERING PRINCIPLES

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