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Percolation and Universality
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
2013 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

In this thesis a detailed discussion of the topic percolation theory in squared lattices in

two dimensions will be conducted. To support this discussion numerical calculations will

be done. For the data analysis and simulations the Hoshen-Kopelman-Algorithm [2] will

be used. All concepts deduced will nally lead to the determination of the conductance's

exponent

t in random resistor networks. Using Derrida's transfer matrix program to

calculate the conductivity of random resistors in two and three dimensions [11] and

the nite-size scaling approach were used. In two dimensions

t= = 0:955 0:006 was

obtained. Were

is the exponent of the correlation length in innite lattices. This

value is in excellent agreement with Derrida (

t= = 0:960:02, [11]) and slightly smaller

than Sahimi (

t= = 0:97480:001, [21]). In three dimensions the same approach yielded

t=

= 2:155 0:012 which some what smaller than the value found by Sahimi t= =

2

:27 0:20 [21] and Gingold and Lobb t= = 2:276 0:012 [25].

Place, publisher, year, edition, pages
2013. , 27 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-127452OAI: oai:DiVA.org:kth-127452DiVA: diva2:644350
Supervisors
Available from: 2013-08-30 Created: 2013-08-30 Last updated: 2013-08-30Bibliographically approved

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