DISORDERATFIRST-ORDERCLASSICALANDQUANTUMPHASE TRANSITIONS by AHMEDKHALILIBRAHIM ADISSERTATION PresentedtotheGraduateFacultyofthe MISSOURIUNIVERSITYOFSCIENCEANDTECHNOLOGY InPartialFulfillmentoftheRequirementsfortheDegree DOCTOROFPHILOSOPHY in PHYSICS 2018 Approvedby Dr. ThomasVojta,Advisor Dr. GeraldWilemski Dr. PaulE.Parris Dr. AleksandrChernatynskiy Dr. JoséA.Hoyos Copyright2018 AHMEDKHALILIBRAHIM AllRightsReserved iii PUBLICATIONDISSERTATIONOPTION Thisdissertationhasbeenpreparedintheformoffourpapers: Paper I, 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)withHatemBarghathiandThomasVojta. Paper II, 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)withThomasVojta. 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)withThomasVojta. Paper IV, Pages 107–127, is a manuscript ready to be published as Numerical investigation of a disordered superconductor-metal quantum phase transition (2018) with ThomasVojta. 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 focusesonfourseparatebutrelatedprojects. First,weinvestigatetheinfluenceofquenched 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 changestheuniversalityclassofthetransition. 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 quantumAshkin-Tellermodelbylarge-scaleMonteCarlosimulations. Wefindthatdisorder rounds the first-order quantum phase transition just as in the classical case. The resulting criticalbehaviordependsonthestrengthoftheinter-colorcouplinginthequantumAshkin- 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- randomtypeandbelongstotherandomtransverse-fieldIsinguniversalityclassaspredicted bystrongdisorderrenormalizationgroupresults. v ACKNOWLEDGMENTS First of all, I would like to express my deepest thanks and gratitude to my advisor Dr. ThomasVojta,forhispatienceanddedicationinsupportingandguidingmethroughout thePhDstudyperiodandwritingmydissertation. Ibelievethisworkwouldnothavebeen possiblewithouthisassistanceandsupport. Thankyou,Dr. Vojta. Iamgreatlyindebtedtoallmyadvisorycommitteemembers,Dr. GeraldWilemski, Dr. Paul Parris, Dr. Aleksandr Chernatynskiy, and Dr. José A. Hoyos, for their valuable discussionsandaccessibility. 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 IraqforgrantingmeaPhDscholarship. Iwouldlikeespeciallytogivemythankstomyfriend,Dr. HatemBarghathi. Thank youforyourhelpandsupport. A special thanks to my family, my parents, my brothers, and my sister. Thank you foryourlove,support,andencouragement. 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 yourpatience,care,andsupport. vi TABLEOFCONTENTS Page PUBLICATIONDISSERTATIONOPTION...................................... iii ABSTRACT .................................................................. iv ACKNOWLEDGMENTS ...................................................... v LISTOFILLUSTRATIONS.................................................... x LISTOFTABLES............................................................. xv SECTION 1. INTRODUCTION.......................................................... 1 1.1. THERMALANDQUANTUMPHASETRANSITIONS ..................... 1 1.1.1. LandauTheoryofPhaseTransitions ................................... 2 1.1.2. TheScalingHypothesisandRenormalizationGroup ................. 6 1.1.3. QuantumPhaseTransitions ............................................. 10 1.1.4. Transverse-FieldIsingModel........................................... 15 1.2. NON-EQUILIBRIUMPHASETRANSITIONS............................... 16 1.3. FINITE-SIZESCALING ........................................................ 19 1.4. DISORDEREDPHASETRANSITIONS ...................................... 22 1.4.1. QuenchedDisorder...................................................... 23 1.4.2. Imry-MaCriterion....................................................... 24 1.4.3. HarrisCriterion.......................................................... 25 1.4.4. Strong-DisorderRenormalizationGroupTheoryandInfiniteRan- domnessCriticalPoint .................................................. 27 vii 1.4.5. Rare-RegionsandGriffithsEffects ..................................... 32 PAPER I. ENHANCEDRARE-REGIONEFFECTSINTHECONTACTPROCESSWITH LONG-RANGECORRELATEDDISORDER................................. 35 ABSTRACT ............................................................................ 35 1. INTRODUCTION ............................................................... 36 2. CONTACTPROCESSWITHCORRELATEDDISORDER.................. 37 3. THEORY ......................................................................... 39 3.1. RARE-REGIONPROBABILITY...................................... 39 3.2. GRIFFITHSPHASE .................................................... 41 3.3. CRITICALPOINT...................................................... 44 4. MONTE-CARLOSIMULATIONS............................................. 47 4.1. OVERVIEW ............................................................. 47 4.2. RESULTS:CRITICALBEHAVIOR................................... 48 4.3. RESULTS:GRIFFITHSPHASE....................................... 54 5. GENERALIZATIONS........................................................... 56 5.1. HIGHERDIMENSIONS ............................................... 56 5.2. OTHERSYSTEM....................................................... 57 6. CONCLUSIONS................................................................. 60 ACKNOWLEDGEMENTS............................................................ 61 REFERENCES ......................................................................... 62 II. EMERGING CRITICAL BEHAVIOR AT A FIRST-ORDER PHASE TRAN- SITIONROUNDEDBYDISORDER........................................ 65 ABSTRACT ............................................................................ 65 1. INTRODUCTION ............................................................... 66 viii 2. DILUTEDASHKIN-TELLERMODEL........................................ 67 3. MONTECARLOSIMULATIONS ............................................. 70 3.1. METHODANDOVERVIEW.......................................... 70 3.2. RESULTS................................................................ 71 4. SUMMARYANDCONCLUSIONS ........................................... 75 ACKNOWLEDGEMENTS............................................................ 77 REFERENCES ......................................................................... 78 III. MONTECARLOSIMULATIONSOFTHEDISORDEREDTHREE-COLOR QUANTUMASHKIN-TELLERCHAIN ..................................... 82 ABSTRACT ............................................................................ 82 1. INTRODUCTION ............................................................... 83 2. MODELANDTHEORY........................................................ 85 2.1. QUANTUMASHKIN-TELLERCHAIN.............................. 85 2.2. RENORMALIZATIONGROUPPREDICTIONS .................... 86 2.3. QUANTUM-TO-CLASSICALMAPPING ............................ 88 3. MONTECARLOSIMULATIONS ............................................. 89 3.1. OVERVIEW ............................................................. 89 3.2. WEAKCOUPLINGREGIME ......................................... 91 3.3. STRONGCOUPLINGREGIME....................................... 96 4. CONCLUSIONS................................................................. 99 ACKNOWLEDGEMENTS............................................................ 101 REFERENCES ......................................................................... 102 IV. NUMERICALINVESTIGATIONOFADISORDEREDSUPERCONDUCTOR- METALQUANTUMPHASETRANSITION................................. 107 ABSTRACT ............................................................................ 107 ix 1. INTRODUCTION ............................................................... 108 2. THEMODEL .................................................................... 109 3. THEORY ......................................................................... 111 3.1. RENORMALIZATIONGROUPPREDICTIONS .................... 111 4. MONTECARLOSIMULATIONS ............................................. 113 5. THERMODYNAMICS.......................................................... 113 5.1. CLEANSYSTEM....................................................... 113 5.2. DISORDEREDSYSTEM............................................... 117 6. CONCLUSIONS................................................................. 122 ACKNOWLEDGEMENTS............................................................ 123 REFERENCES ......................................................................... 124 SECTION 2. CONCLUSIONSANDOUTLOOK..........................................128 REFERENCES................................................................130 VITA.........................................................................134 x LISTOFILLUSTRATIONS Figure Page SECTION 1.1. Schematic phase diagram of water. The solid lines indicate first-order phase transitions. The gas-liquid phase boundary ends in a critical point at which the phase transition is continuous. The intersection of three lines is referred toasthetriplepointatwhichallthreephasescoexist. ............................. 2 1.2. Schematic of magnetization m vs. temperature T at a ferromagnetic phase transition. If the temperature T is below the critical temperature T , the c substancehasafinite(non-zero)valueofthemagnetizationm (ferromagnetic phase). WhenT > T ,thenthemagnetization m vanishes(paramagneticphase). 3 c 1.3. Schematic of the Landau free energy F as a function of the order parameter L m forvariousvalueofr. ............................................................. 4 1.4. Schematic phase diagram in the vicinity of a quantum critical point (QCP) located at P . The horizontal axis is the non-thermal control parameter P c which can changes the system by means of the zero-temperature (quantum) phasetransition,whiletheverticalaxisisthetemperatureT. Thesolidlineis the boundary between finite-temperature phases, near to this line the critical behaviorisclassical. Thedashedlinesarethebordersofthequantumcritical regionthenaregivenby k T ∼ (cid:126)w ................................................. 12 B c 1.5. Schematic of contact process in one-dimension. Infected (active) sites infect their neighbors at rate λ/2. Active sites can spontaneously become inactive (healthy)withhealingrate µ......................................................... 18 1.6. Schematic of Binder cumulant g vs. temperature T for different system size L in classical Ising model. All curves cross at the same temperature that correspondstoacriticaltemperatureT ............................................. 21 c 1.7. BehaviorofBindercumulantintherandomquantumIsingmodel. (a)Binder cumulant as a function of L for several L at the critical temperature. (b) τ Scaling plot of the Binder cumulant at T . Main panel: Power-law scaling g c vs L /Lmax. Inset: Activatedscaling g vsln(L )/ln(Lmax)........................ 22 τ τ τ τ 1.8. SchematicoftheImry-Macriterian. ................................................ 25 1.9. SchematicofHarriscriterian. ....................................................... 26 1.10. Schematic of the strong-disorder renormalization group step for decimating a field.................................................................................... 29