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Disorder at First-Order Classical and Quantum Phase Transitions

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Disorder at First-Order Classical and Quantum Phase Transitions DISORDER AT FIRST-ORDER CLASSICAL AND QUANTUM PHASE TRANSITIONS by AHMED KHALIL IBRAHIM A DISSERTATION Presented to the Graduate Faculty of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY in PHYSICS 2018 Approved by Dr. Thomas Vojta, Advisor Dr. Gerald Wilemski Dr. Paul E. Parris Dr. Aleksandr Chernatynskiy Dr. José A. Hoyos Copyright 2018 AHMED KHALIL IBRAHIM All Rights Reserved iii PUBLICATION DISSERTATION OPTION This dissertation has been prepared in the form of four papers: PaperI, Pages 35–64, has been published as Enhanced rare-region effects in the contact process with long-range correlated disorder, published in Physical Review E 90, 042132 (2014) with Hatem Barghathi and Thomas Vojta. PaperII, Pages 65–81, has been published as Emerging critical behavior at a first-order phase transition rounded by disorder, published in Fortschritte der Physik 65, 1600018 (2017) with Thomas Vojta. Paper III, Pages 82–106, has been published as Monte Carlo simulations of the disordered three-color quantum Ashkin-Teller chain, published in Physical Review B 95, 054403 (2017) with Thomas Vojta. PaperIV, Pages 107–127, is a manuscript ready to be published as Numerical investigation of a disordered superconductor-metal quantum phase transition (2018) with Thomas Vojta. In addition, the dissertation contains an introductory section (Sec.1) and a brief summary (Sec.2). iv ABSTRACT This dissertation studies the effects of quenched disorder on classical, quantum and nonequilibrium phase transitions. After a short introduction which covers the basic concepts of phase transitions, finite-size scaling and random disorder, the dissertation focuses on four separate but related projects. First, we investigate the influence of quenched disorder with long-range spatial correlations on the nonequilibrium phase transitions in the contact process. We show that the long-range correlations increase the probability to find rare atypical regions in the sample. This leads to enhanced Griffiths singularities and changes the universality class of the transition. Project 2 and 3 focus on disorder at first-order phase transitions. In project 2, we analyze the phase transitions of a classical Ashkin-Teller magnet. We demonstrate that the first-order classical phase transition is destroyed by disorder, and the resulting continuous transition belongs to the clean two-dimensional Ising universality class with logarithmic corrections. Project 3 investigates the fate of the first-order quantum phase transition in the quantum Ashkin-Teller model by large-scale Monte Carlo simulations. We find that disorder rounds the first-order quantum phase transition just as in the classical case. The resulting critical behavior depends on the strength of the inter-color coupling in the quantum Ashkin- Teller model. This leads to two different regimes, the weak and strong coupling regimes, both of which feature infinite-randomness critical behavior but in different universality classes. Finally, we study the quantum phase transition of a disordered nanowire from superconductor to metallic behavior. We show that the critical behavior is of infinite- random type and belongs to the random transverse-field Ising universality class as predicted by strong disorder renormalization group results. v ACKNOWLEDGMENTS First of all, I would like to express my deepest thanks and gratitude to my advisor Dr. Thomas Vojta, for his patience and dedication in supporting and guiding me throughout the PhD study period and writing my dissertation. I believe this work would not have been possible without his assistance and support. Thank you, Dr. Vojta. I am greatly indebted to all my advisory committee members, Dr. Gerald Wilemski, Dr. Paul Parris, Dr. Aleksandr Chernatynskiy, and Dr. José A. Hoyos, for their valuable discussions and accessibility. I would like to thank our former chairman, Dr. George D. Waddill, our graduate coordinator, Dr. Jerry Peacher, and also the staff in the Physics Department, Pamela J. Crabtree, Janice Gargus, Russell L. Summers, Ronald Woody, and Andy Stubbs, for their help. I am very thankful to the Higher Committee for Education Development (HCED) in Iraq for granting me a PhD scholarship. I would like especially to give my thanks to my friend, Dr. Hatem Barghathi. Thank you for your help and support. A special thanks to my family, my parents, my brothers, and my sister. Thank you for your love, support, and encouragement. Finally, I would like to express my gratitude to my beloved wife, Raghdaa "Um Raneem", and my wonderful daughters, Raneem, Rafeef, and Taleen. Thank you, for all your patience, care, and support. vi TABLE OF CONTENTS Page PUBLICATION DISSERTATION OPTION . iii ABSTRACT.................................................................. iv ACKNOWLEDGMENTS . .v LIST OF ILLUSTRATIONS . .x LIST OF TABLES . xv SECTION 1. INTRODUCTION. .1 1.1. THERMAL AND QUANTUM PHASE TRANSITIONS .....................1 1.1.1. Landau Theory of Phase Transitions ...................................2 1.1.2. The Scaling Hypothesis and Renormalization Group .................6 1.1.3. Quantum Phase Transitions ............................................. 10 1.1.4. Transverse-Field Ising Model ........................................... 15 1.2. NON-EQUILIBRIUM PHASE TRANSITIONS ............................... 16 1.3. FINITE-SIZE SCALING ........................................................ 19 1.4. DISORDERED PHASE TRANSITIONS ...................................... 22 1.4.1. Quenched Disorder ...................................................... 23 1.4.2. Imry-Ma Criterion ....................................................... 24 1.4.3. Harris Criterion.......................................................... 25 1.4.4. Strong-Disorder Renormalization Group Theory and Infinite Ran- domness Critical Point .................................................. 27 vii 1.4.5. Rare-Regions and Griffiths Effects ..................................... 32 PAPER I. ENHANCED RARE-REGION EFFECTS IN THE CONTACT PROCESS WITH LONG-RANGE CORRELATED DISORDER. 35 ABSTRACT ............................................................................ 35 1. INTRODUCTION ............................................................... 36 2. CONTACT PROCESS WITH CORRELATED DISORDER.................. 37 3. THEORY ......................................................................... 39 3.1. RARE-REGION PROBABILITY ...................................... 39 3.2. GRIFFITHS PHASE .................................................... 41 3.3. CRITICAL POINT ...................................................... 44 4. MONTE-CARLO SIMULATIONS ............................................. 47 4.1. OVERVIEW ............................................................. 47 4.2. RESULTS: CRITICAL BEHAVIOR ................................... 48 4.3. RESULTS: GRIFFITHS PHASE ....................................... 54 5. GENERALIZATIONS........................................................... 56 5.1. HIGHER DIMENSIONS ............................................... 56 5.2. OTHER SYSTEM ....................................................... 57 6. CONCLUSIONS ................................................................. 60 ACKNOWLEDGEMENTS ............................................................ 61 REFERENCES ......................................................................... 62 II. EMERGING CRITICAL BEHAVIOR AT A FIRST-ORDER PHASE TRAN- SITION ROUNDED BY DISORDER . 65 ABSTRACT ............................................................................ 65 1. INTRODUCTION ............................................................... 66 viii 2. DILUTED ASHKIN-TELLER MODEL........................................ 67 3. MONTE CARLO SIMULATIONS ............................................. 70 3.1. METHOD AND OVERVIEW .......................................... 70 3.2. RESULTS................................................................ 71 4. SUMMARY AND CONCLUSIONS ........................................... 75 ACKNOWLEDGEMENTS ............................................................ 77 REFERENCES ......................................................................... 78 III. MONTE CARLO SIMULATIONS OF THE DISORDERED THREE-COLOR QUANTUM ASHKIN-TELLER CHAIN . 82 ABSTRACT ............................................................................ 82 1. INTRODUCTION ............................................................... 83 2. MODEL AND THEORY ........................................................ 85 2.1. QUANTUM ASHKIN-TELLER CHAIN .............................. 85 2.2. RENORMALIZATION GROUP PREDICTIONS .................... 86 2.3. QUANTUM-TO-CLASSICAL MAPPING ............................ 88 3. MONTE CARLO SIMULATIONS ............................................. 89 3.1. OVERVIEW ............................................................. 89 3.2. WEAK COUPLING REGIME ......................................... 91 3.3. STRONG COUPLING REGIME ....................................... 96 4. CONCLUSIONS ................................................................. 99 ACKNOWLEDGEMENTS ............................................................ 101 REFERENCES ......................................................................... 102 IV. NUMERICAL INVESTIGATION OF A DISORDERED SUPERCONDUCTOR- METAL QUANTUM PHASE TRANSITION . 107 ABSTRACT ............................................................................ 107 ix 1. INTRODUCTION
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