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The | 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]]. | ||
== Definition == | |||
Frequently in [[physics]] one comes across situations where [[Quenched disorder|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 [...] denotes averaging over realisations (“averaging over samples”) provided the [[relative variance]] ''R''<sub>''X''</sub> = ''V''<sub>''X''</sub> / [''X'']<sup>2</sup> → 0 for large ''X'', where ''V''<sub>''X''</sub> = [''X''<sup>2</sup>] − [''X'']<sup>2</sup>. 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 ''R''<sub>''X''</sub> ~ ''N''<sup>−1</sup> thereby ensuring self-averaging. On the other hand, at the critical point, the question whether <math>X</math> is self-averaging or not becomes nontrivial, due to long range [[correlation]]s. | |||
== Non self-averaging systems == | |||
At the pure critical point randomness is classified as relevant if, by the standard definition of relevance, it leads to a change in the critical behaviour (i.e., the critical exponents) of the pure system. It has been shown by recent renormalization group and [[numerical methods|numerical studies]] that self-averaging property is lost if randomness or disorder is relevant.<ref>{{cite journal | |||
| author = -A. Aharony and A.B. Harris | |||
| year = 1996 | |||
| month = | |||
| title = Absence of Self-Averaging and Universal Fluctuations in Random Systems near Critical Points | |||
| journal = Phys. Rev. Lett. | |||
| volume = 77 | |||
| issue = 18 | |||
| pages = 3700 | |||
| doi = 10.1103/PhysRevLett.77.3700 | |||
| id = | |||
| url = | |||
| format = | |||
| accessdate = | |||
| pmid = 10062286 | |||
| bibcode=1996PhRvL..77.3700A}}</ref> Most importantly as N → ∞, R<sub>X</sub> at the critical point approaches a constant. Such systems are called non self-averaging. Thus unlike the self-averaging scenario, numerical simulations cannot lead to an improved picture in larger lattices (large N), even if the critical point is exactly known. In summary, various types of self-averaging can be indexed with the help of the [[asymptotic]] size dependence of a quantity like R<sub>X</sub>. If R<sub>X</sub> falls off to zero with size, it is self-averaging whereas if R<sub>X</sub> approaches a constant as N → ∞, the system is non-self-averaging. | |||
==Strong and weak self-averaging== | |||
There is a further classification of self-averaging systems as strong and weak. If the exhibited behavior is ''R''<sub>''X''</sub> ~ ''N''<sup>−1</sup> as suggested by the central limit theorem, mentioned earlier, the system is said to be strongly self-averaging. Some systems shows a slower [[power law]] decay ''R''<sub>''X''</sub> ~ ''N''<sup>−''z''</sup> with 0 < ''z'' < 1. Such systems are classified weakly self-averaging. The known critical exponents of the system determine the exponent ''z''. | |||
It must also be added that relevant randomness does not necessarily imply non self-averaging, especially in a mean-field scenario. | |||
<ref>{{cite journal | |||
| author = - S Roy and SM Bhattacharjee | |||
| year = 2006 | |||
| month = | |||
| title = Is small-world network disordered? | |||
| journal = Physics Letters A | |||
| volume = 352 | |||
| issue = | |||
| pages = 13 | |||
| doi = 10.1016/j.physleta.2005.10.105 | |||
| id = | |||
| url = | |||
| format = | |||
| accessdate = | |||
|bibcode = 2006PhLA..352...13R |arxiv = cond-mat/0409012 }}</ref> | |||
The RG arguments mentioned above need to be extended to situations with sharp limit of ''T''<sub>''c''</sub> distribution and long range interactions. | |||
== References == | |||
<references/> | |||
[[Category:Statistical mechanics]] | |||
Latest revision as of 00:29, 24 October 2013
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.
Definition
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 [...] denotes 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 is self-averaging or not becomes nontrivial, due to long range correlations.
Non self-averaging systems
At the pure critical point randomness is classified as relevant if, by the standard definition of relevance, it leads to a change in the critical behaviour (i.e., the critical exponents) of the pure system. It has been shown by recent renormalization group and numerical studies that self-averaging property is lost if randomness or disorder is relevant.[1] Most importantly as N → ∞, RX at the critical point approaches a constant. Such systems are called non self-averaging. Thus unlike the self-averaging scenario, numerical simulations cannot lead to an improved picture in larger lattices (large N), even if the critical point is exactly known. In summary, various types of self-averaging can be indexed with the help of the asymptotic size dependence of a quantity like RX. If RX falls off to zero with size, it is self-averaging whereas if RX approaches a constant as N → ∞, the system is non-self-averaging.
Strong and weak self-averaging
There is a further classification of self-averaging systems as strong and weak. If the exhibited behavior is RX ~ N−1 as suggested by the central limit theorem, mentioned earlier, the system is said to be strongly self-averaging. Some systems shows a slower power law decay RX ~ N−z with 0 < z < 1. Such systems are classified weakly self-averaging. The known critical exponents of the system determine the exponent z.
It must also be added that relevant randomness does not necessarily imply non self-averaging, especially in a mean-field scenario. [2] The RG arguments mentioned above need to be extended to situations with sharp limit of Tc distribution and long range interactions.
References
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The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
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Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang