Self-Averaging
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A self-averaging physical property of a disordered system is one that can be described by averaging over a sufficiently large sample. The concept was introduced by Ilya Mikhailovich Lifshitz.Frequently in physics one comes across situations where quenched randomness plays an important role. Any physical property X of such a system, would require an averaging over all disorder realisations. The system can be completely described by the average [X] where [cdots] denotes…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A self-averaging physical property of a disordered system is one that can be described by averaging over a sufficiently large sample. The concept was introduced by Ilya Mikhailovich Lifshitz.Frequently in physics one comes across situations where quenched randomness plays an important role. Any physical property X of such a system, would require an averaging over all disorder realisations. The system can be completely described by the average [X] where [cdots] denotes an averaging over realisations ( averaging over samples ) provided the relative variance RX = VX/[X]2 0 for large X, where VX = [X2] [X]2. In such a scenario a single large system is sufficient to represent the whole ensemble. Such quantities are called self-averaging. Away from criticality, when the larger lattice is built from smaller blocks, then due to the additivity property of an extensive quantity, the central limit theorem guarantees that RX N 1 thereby ensuring self-averaging. On the other hand, at the critical point, the question whether X is self-averaging or not becomes nontrivial, due to long range correlations.