Bond-disordered spin systems: Theory and application to doped high-Tc compounds

Abstract

We examine the stability of magnetic order in a classical Heisenberg model with quenched random exchange couplings. This system represents the spin degrees of freedom in high-$T_{\text{c}}$ compounds with immobile dopants. Starting from a replica representation of the nonlinear $\sigma$-model, we perform a renormalization-group analysis. The importance of cumulants of the disorder distribution to arbitrarily high orders necessitates a functional renormalization scheme. From the renormalization flow equations we determine the magnetic correlation length numerically as a function of the impurity concentration and of temperature. From our analysis follows that two-dimensional layers can be magnetically ordered for arbitrarily strong but sufficiently diluted defects. We further consider the dimensional crossover in a stack of weakly coupled layers. The resulting phase diagram is compared with experimental data for La${}_{2-x}$Sr${}_x$CuO${}_4$.

12 pages, 5 figures

References in corpus (5)

• Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-εdimensions
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Cited by in corpus (2)

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