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A Matter of Disorder: Monte Carlo Simulations of Phase Transitions in Strongly Disordered Systems
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Phase transitions and their critical scaling properties, especially in systems with disorder, are important both for our theoretical understanding of our environment, but also for their practical use in applications and materials in our everyday life. This thesis presents results from finite size scaling analysis of critical phenomena in systems with disorder, using high-precision Monte Carlo simulations and state of the art numerical methods. Specifically, theoretical models suitable for simulations in the presence of uncorrelated or correlated disorder are studied.

Uncorrelated strong disorder, as present in the two dimensional gauge glass model to study the vortex glass phase of high temperature superconductors in an applied magnetic field is shown to lack a finite temperature phase transition. Further, results from dynamic quantities, such as resistance and autocorrelation functions, indicate the existence of two distinct diverging correlation times, one associated with local relaxation and one associated with vortex phase slips.

Correlated disorder is studied both in the superfluid transition of helium-4 and in the anisotropic critical scaling of a transverse Meissner-like transition in an experimental setup of a high temperature superconductor. For the superfluid helium transition, it is shown that the presence of fractally correlated disorder presumably alters the universality class of the pure model. Also, a comparison with experimental data suggests that the critical scaling theory describing the heat capacity of helium-4 may need to be modified in the presence of the disorder. In the case of superconductors, analyzing experimental data from resistance measurements in a system with columnar defects together with an anisotropy in the applied magnetic field, reveals a fully anisotropic scaling regime.

Finally, a data analysis is presented from simulations of a charged particle gas system in three dimensions, where the normal Coulomb interaction between charges is changed into a logarithmic interaction. Previous work indicates the possibility of a transition similar to the Kosterlitz-Thouless transition in certain two dimensional systems. On the contrary, our simulations seem to favor a system whose critical scaling behavior is consistent with a transition occurring only at zero critical temperature.

Overall, disorder in the model systems studied leads to important modifications of the critical scaling properties of pure systems, and thereby also to possible changes of the corresponding universality classes. This results in interesting predictions with experimentally relevant consequences.

Place, publisher, year, edition, pages
Stockholm: KTH , 2007. , vi, 63 p.
Series
Trita-FYS, ISSN 0280-316X ; 2007:19
Keyword [en]
phase transitions, disorder, Monte Carlo simulations, superconductivity
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:kth:diva-4313ISBN: 978-91-7178-600-5 (print)OAI: oai:DiVA.org:kth-4313DiVA: diva2:11755
Public defence
2007-03-30, The Svedbergsalen, AlbaNova, KTH, 106 91, Stockholm, 10:15
Opponent
Supervisors
Note
QC 20100811Available from: 2007-03-21 Created: 2007-03-21 Last updated: 2010-08-11Bibliographically approved
List of papers
1. Zero-temperature glass transition in the two-dimensional gauge glass model
Open this publication in new window or tab >>Zero-temperature glass transition in the two-dimensional gauge glass model
2004 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 69, no 18, 184512-1 p.Article in journal (Refereed) Published
Abstract [en]

We investigate dynamic scaling properties of the two-dimensional gauge glass model for the vortex glass phase in superconductors with quenched disorder. From extensive Monte Carlo simulations we obtain static and dynamic finite-size scaling behavior, where the static simulations use a temperature exchange method to ensure convergence at low temperatures. Both static and dynamic scaling of Monte Carlo data is consistent with a glass transition at zero temperature, with correlation length exponent given by 1/nu=0.36+/-0.03. We study a dynamic correlation function for the superconducting order parameter, as well as the phase slip resistance. From the scaling of these two functions, we find evidence for two distinct diverging correlation times at the zero-temperature glass transition. The longer of these time scales is associated with phase slip fluctuations across the system that lead to finite resistance at any finite temperature. The shorter time scale can be described by the form tausimilar toxi(z), with a dynamic exponent z=2.7+/-0.2, and corresponds to local phase fluctuations.

Keyword
PHASE-TRANSITION; SPIN-GLASS; VORTEX; SUPERCONDUCTORS; DISORDER
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-6906 (URN)10.1103/PhysRevB.69.184512 (DOI)000222095500067 ()2-s2.0-42749098095 (Scopus ID)
Note
QC 20100811Available from: 2007-03-21 Created: 2007-03-21 Last updated: 2012-03-21Bibliographically approved
2. Critical scaling properties at the superfluid transition of He-4 in aerogel
Open this publication in new window or tab >>Critical scaling properties at the superfluid transition of He-4 in aerogel
2006 (English)In: Physical Review Letters, ISSN 0031-9007, Vol. 97, no 22, 225702- p.Article in journal (Refereed) Published
Abstract [en]

We study the superfluid transition of He-4 in aerogel by Monte Carlo simulations and finite size scaling analysis. Aerogel is a highly porous silica glass, which we model by a diffusion limited cluster aggregation model. The superfluid is modeled by a three dimensional XY model, with excluded bonds to sites on the aerogel cluster. We obtain the correlation length exponent nu=0.73 +/- 0.02, in reasonable agreement with experiments and with previous simulations. For the heat capacity exponent alpha, both experiments and previous simulations suggest deviations from the Josephson hyperscaling relation alpha=2-d nu. In contrast, our Monte Carlo results support hyperscaling with alpha=-0.2 +/- 0.05. We suggest a reinterpretation of the experiments, which avoids scaling violations and is consistent with our simulation results.

Keyword
Aerogels; Computer simulation; Fused silica; Monte Carlo methods; Phase transitions; Specific heat; Correlation length; Hyperscaling relation; Porous silica glass; Superfluid transition; Superfluid helium
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-6907 (URN)10.1103/PhysRevLett.97.225702 (DOI)000242538700034 ()2-s2.0-34547647871 (Scopus ID)
Note
QC 20100811Available from: 2007-03-21 Created: 2007-03-21 Last updated: 2012-03-21Bibliographically approved
3. Fully anisotropic superconducting transition in ion-irradiated YBa2Cu3O7-delta with a tilted magnetic field
Open this publication in new window or tab >>Fully anisotropic superconducting transition in ion-irradiated YBa2Cu3O7-delta with a tilted magnetic field
Show others...
2007 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 75, no 10, 100504- p.Article in journal (Refereed) Published
Abstract [en]

We consider the superconducting vortex solid-to-liquid transition in heavy ion-irradiated untwinned YBa2Cu3O7-delta single crystals in the case where the magnetic field direction does not coincide with that of the irradiation-induced linear columnar defects. For a certain range of angles, the resistivities measured in three orthogonal spatial directions vanish at the transition as three clearly different powers of reduced temperature. At previously known second-order phase transitions, scaling of physical quantities has either been isotropic or anisotropic in one direction. Thus, our findings yield evidence for a new type of critical behavior with fully anisotropic critical exponents.

Keyword
high-temperature superconductors, bose-glass-transition, correlated disorder, columnar defects, single-crystals, localization, vortices, phase
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-16498 (URN)10.1103/PhysRevB.75.100504 (DOI)000245329100009 ()2-s2.0-33947515033 (Scopus ID)
Note
QC 20100811Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
4. Monte Carlo Simulations of a Lattice Gas with Logarithmic Interactions
Open this publication in new window or tab >>Monte Carlo Simulations of a Lattice Gas with Logarithmic Interactions
(English)Manuscript (Other academic)
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-6909 (URN)
Note
QC 20100811Available from: 2007-03-21 Created: 2007-03-21 Last updated: 2010-08-11Bibliographically approved

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