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Les études in Ising field theory and related problems
Descriptive
TitleInfo
Title
Les études in Ising field theory and related problems
Name
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Ziyatdinov
NamePart
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Iskander
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Iskander Ziyatdinov
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author
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Zamolodchikov
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(type = given)
Alexander
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Alexander Zamolodchikov
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Advisory Committee
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chair
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Goldin
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Gerald
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Gerald Goldin
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Advisory Committee
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internal member
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Lath
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Amitabh
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Amitabh Lath
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Advisory Committee
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internal member
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Lukyanov
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Sergei
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Sergei Lukyanov
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Advisory Committee
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internal member
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Tsvelik
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Alexei
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Alexei Tsvelik
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Advisory Committee
Role
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outside member
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Rutgers University
Role
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(authority = RULIB)
degree grantor
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NamePart
Graduate School - New Brunswick
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school
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Text
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theses
OriginInfo
DateCreated
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2011
DateOther
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(type = degree)
2011-05
Place
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xx
Language
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(type = code)
eng
Subject
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Topic
Physics and Astronomy
Subject
(authority = ETD-LCSH)
Topic
Ising model
Subject
(authority = ETD-LCSH)
Topic
Quantum chromodynamics
Subject
(authority = ETD-LCSH)
Topic
Ferromagnetism
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
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ETD_3179
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electronic resource
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Extent
ix, 66 p. : ill.
Note
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Ph.D.
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Includes bibliographical references
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Includes vita
Note
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by Iskander Ziyatdinov
Identifier
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http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000061645
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Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier
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rucore19991600001
Abstract
The main subject of this thesis is the Ising field theory, the field theory describing the scaling limit of the two-dimensional Ising model near its critical point. We study the Ising field theory in low- and high-temperature regimes.
In the low-temperature regime we address questions related to the mass spectrum of the bound states that exist in the theory. The overall goal is to study analytic properties of the masses taken as functions of the scaling variable in the theory. At this stage, we are primarily interested in the asymptotic series in the coupling parameter. We describe methods used for developing expansions in the coupling parameter when this parameter is sufficiently small. This gives rise to the low-energy and semiclassical series. Methods developed are then applied to a different model, a model that has many things in common with the Ising field theory, the two-dimensional quantum chromodynamics with infinite number of colors, also known as the ‘t Hooft model.
In the second part of the thesis we turn to the Ising field theory in the high- temperature regime. Here we study the problem of scattering in a weak magnetic field. We compute the leading perturbative correction to the scattering amplitude for the 2 -> 2 process. This is done first by means of standard methods based on the direct intermediate-state decomposition and dispersion relations. Then we compute the large energy asymptotic of the amplitude for this process directly using a known relation between the Ising field theory at zero magnetic field and classical sinh-Gordon equation. We obtain consistent results that show the logarithmic growth of the amplitude with energy at this order in magnetic field. Going beyond the leading order we argue that at large energies for a sufficiently weak magnetic field the amplitude exhibits a power-like decay.
In the low-temperature regime we address questions related to the mass spectrum of the bound states that exist in the theory. The overall goal is to study analytic properties of the masses taken as functions of the scaling variable in the theory. At this stage, we are primarily interested in the asymptotic series in the coupling parameter. We describe methods used for developing expansions in the coupling parameter when this parameter is sufficiently small. This gives rise to the low-energy and semiclassical series. Methods developed are then applied to a different model, a model that has many things in common with the Ising field theory, the two-dimensional quantum chromodynamics with infinite number of colors, also known as the ‘t Hooft model.
In the second part of the thesis we turn to the Ising field theory in the high- temperature regime. Here we study the problem of scattering in a weak magnetic field. We compute the leading perturbative correction to the scattering amplitude for the 2 -> 2 process. This is done first by means of standard methods based on the direct intermediate-state decomposition and dispersion relations. Then we compute the large energy asymptotic of the amplitude for this process directly using a known relation between the Ising field theory at zero magnetic field and classical sinh-Gordon equation. We obtain consistent results that show the logarithmic growth of the amplitude with energy at this order in magnetic field. Going beyond the leading order we argue that at large energies for a sufficiently weak magnetic field the amplitude exhibits a power-like decay.
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Identifier
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doi:10.7282/T30864KD
Genre
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ETD doctoral
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Rights
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The author owns the copyright to this work.
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Name
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Ziyatdinov
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Iskander
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Copyright Holder
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Permission or license
DateTime
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2011-03-09 12:15:28
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Name
Iskander Ziyatdinov
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Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
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License
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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