Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2001-10-02
Phys. Rev. B 65, 224502 (2002)
Physics
Condensed Matter
Disordered Systems and Neural Networks
12 pages, 5 figures
Scientific paper
10.1103/PhysRevB.65.224502
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-$T_\textrm{c}$ 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$_4$.
Krüger Frank
Scheidl Stefan
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