Lack of Self Averaging and Finite Size Scaling in Critical Disordered Systems

Details Lack of Self Averaging and Finite Size Scaling in Critical Disordered Systems Lack of Self Averaging and Finite Size Scaling in Critical Disordered Systems

1998-02-09

arxiv.org/abs/cond-mat/9802095v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 5 figures, typo in title corrected

Scientific paper

We simulated site dilute Ising models in $d=3$ dimensions for several lattice sizes $L$. For each $L$ singular thermodynamic quantities $X$ were measured at criticality and their distributions $P(X)$ were determined, for ensembles of several thousand random samples. For $L \to \infty$ the width of $P(X)$ tends to a universal constant, i.e. there is no self averaging. The width of the distribution of the sample dependent pseudocritical temperatures $T_c(i,L)$ scales as $\delta T_c(L) \sim L^{-1/\nu}$ and NOT as $\sim L^{-d/2}$. Finite size scaling holds; the sample dependence of $X_i(T_c)$ enters predominantly through $T_c(i,L)$.

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