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

S. Wiseman; E. Domany

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arXiv · cond-mat/9802095

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

S. Wiseman·E. Domany

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Abstract

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 $δT_c(L) \sim L^{-1/ν}$ 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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BibTeX RIS

S. Wiseman, E. Domany. 1998-02-10. Lack of Self Averaging and Finite Size Scaling in Critical Disordered Systems. https://arxiv.org/abs/cond-mat/9802095

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