Abstract/Details

Cluster Monte Carlo and network flow algorithms for critical phenomena


2001 2001

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Abstract (summary)

Phase transitions and critical phenomena in several spin models are studied. These models include a two and three dimensional XY model and Ising models in structured and random field. The methods of study are cluster Monte Carlo simulations and network flow optimization algorithms.

The XY model and a related soft spin model belonging to the O(2) universality class are studied using a modified version of the Invaded Cluster algorithm. The static critical properties of the models and the dynamic characteristics of the algorithm are studied. The critical exponent η for the O(2) universality class in two and three dimensions is measured. The Invaded Cluster algorithm for the XY model does not show any critical slowing for global variables.

Benzene adsorption in a nanoporous solid is modeled with an Ising model with both internal and external magnetic fields. The first order phase transition and the critical properties of the system are studied. The system is simulated using the two replica cluster algorithm. The critical temperature of the system is found to decrease with increasing difference of the values of the internal fields. It is found that the system undergoes a phase transition for a relatively wide, experimentally obtainable, region of values of its parameters.

The random field Ising model in three dimensions is studied at zero temperature. The nature of randomness induced phase transition is studied using a numerical network flow optimization method. It is found that the latent heat at the phase transition vanishes in the limit of infinite system size which can be taken as a proof of a second order phase transition.

Indexing (details)


Subject
Condensation
Classification
0611: Condensation
Identifier / keyword
Pure sciences; Cluster Monte Carlo; Critical phenomena; Network flow; Phase transition
Title
Cluster Monte Carlo and network flow algorithms for critical phenomena
Author
Dukovski, Ilija
Number of pages
96
Publication year
2001
Degree date
2001
School code
0118
Source
DAI-B 62/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
0493392068, 9780493392066
Advisor
Machta, Jonathan
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3027193
ProQuest document ID
304700322
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304700322
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