Disordered bosons in one dimension: from weak to strong randomness criticality

We investigate the superfluid-insulator quantum phase transition of one-dimensional bosons with off-diagonal disorder by means of large-scale Monte-Carlo simulations. For weak disorder, we find the transition to be in the same universality class as the superfluid-Mott insulator transition of the clean system. The nature of the transition changes for stronger disorder. Beyond a critical disorder strength, we find nonuniversal, disorder-dependent critical behavior. We compare our results to recent perturbative and strong-disorder renormalization group predictions. We also discuss experimental implications as well as extensions of our results to other systems.Comment: 5 pages, 5 eps figures included, final version as publishe

Modification of smeared phase transitions by spatial disorder correlations

Phase transitions in disordered systems can be smeared if rare spatial regions develop true static order while the bulk system is in the disordered phase. Here, we study the effects of spatial disorder correlations on such smeared phase transitions. The behaviors of observables are determined within optimal fluctuation theory. We show that even short-range correlations can qualitatively modify smeared phase transitions. For positive correlations (like impurity atoms attract each other), the order parameter is enhanced, while it is suppressed for repulsive correlations (like atoms repel each other). We use computer simulations to generate various types of disorder correlations, and to verify our theoretical predictions.Comment: submitted to the Proceedings of the XVII Training Course in the Physics of Strongly Correlated Systems, builds on arXiv:1109.4290, 5 pages, 2 figure

Phase transitions in disordered systems

Disorder can have a wide variety of consequences for the physics of phase transitions. Some transitions remain unchanged in the presence of disorder while others are completely destroyed. In this thesis we study the effects of disorder on several classical and quantum phase transitions in condensed matter systems. After a brief introduction, we study the ferromagnetic phase transition in a randomly layered Heisenberg magnet using large-scale Monte-Carlo simulations. Our results provide numerical evidence for the exotic infinite-randomness scenario. We study classical and quantum smeared phase transitions in substitutional alloys A₁₋ₓBₓ. Our results show that the disorder completely destroys the phase transition with a pronounced tail of the ordered phase developing for all compositions x \u3c 1. In addition, we find that short-ranged disorder correlations can have a dramatic effect on the transition. Moreover, we show an experimental realization of the composition-tuned ferromagnetic-to-paramagnetic quantum phase transition in Sr₁₋ₓCaₓRuO₃. We investigate the effects of disorder on first-order quantum phase transitions on the example of the N-color quantum Ashkin-Teller model. By means of a strong disorder renormalization group, we demonstrate that disorder rounds the first-order transition to a continuous one for both weak and strong coupling between the colors. Finally, we investigate the superfluid-insulator quantum phase transition of one-dimensional bosons with off-diagonal disorder by means of large-scale Monte-Carlo simulations. Beyond a critical disorder strength, we find nonuniversal, disorder-dependent critical behavior --Abstract, page iv

Rounding of a first-order quantum phase transition to a strong-coupling critical point

We investigate the effects of quenched disorder on first-order quantum phase transitions on the example of the $N$-color quantum Ashkin-Teller model. By means of a strong-disorder renormalization group, we demonstrate that quenched disorder rounds the first-order quantum phase transition to a continuous one for both weak and strong coupling between the colors. In the strong coupling case, we find a distinct type of infinite-randomness critical point characterized by additional internal degrees of freedom. We investigate its critical properties in detail, and we discuss broader implications for the fate of first-order quantum phase transitions in disordered systems.Comment: 5 pages, 4 figure

Effects of Molecular Size and Orientation on the Interfacial Properties and Wetting Behavior of Water/ N -Alkane Systems: A Molecular-Dynamics Study

Molecular Dynamics Simulations (MD) Are Performed to Study the Interfacial Structure/tension and Wetting Behavior of Water/n-Alkane Systems (Water/nC5 to Water/nC16 Where nCx = CxH(2x + 2)). in Particular, We Study Complete-To-Partial Wetting Transitions by Changing the N-Alkane Chain Length (NC) at a Constant Temperature, T = 295 K. Simulations Are Carried Out with a United-Atom TraPPE Model for N-Alkanes and the TIP4P-2005 Model of Water. Simulation Results Are in Excellent Agreement with the Initial Spreading Coefficients and Contact Angles Calculated using Experimental Values of the Surface and Interfacial Tensions. in Addition, It Has Been Determined that Water/(nC5-nC7) and Water/(nC8-nC16), Respectively, Exhibit Complete and Partial Initial Wetting Modes. Simulations Show that the Interfacial Structures of Water/(nC5-nC7) Are Different from Water/(nC8-nC16) Systems. in the Latter, Water Preferentially Orients Near the Interface to Increase the Number of Hydrogen Bonds and the Charge and Mass Densities. Moreover, the Orientation of N-Alkane Molecules at Water/(nC8-nC16) Interfaces Has a Long-Range Persistence, Resulting in Layered Structures that Increase with NC. in Addition, Simulation Results of the Orientational Order Parameter Sz Show Alignment Behavior of the N-Alkane Molecules with Respect to the Interfaces. Simulations Predict that the Central Segments of N-Alkane Are Strongly Packed in the Interfaces While the End Segments (Methyl Groups) Form Smaller Peaks in the Outer Edge of the Layer. This Observation Confirms the Horseshoe Or C-Shaped Structure of N-Alkane Molecules in the Water/n-Alkane Interfaces. at Constant Temperature, the Interface Widths of Both Water and the n-Alkanes Decrease with Increasing n-Alkane Molecular Length. These Results Suggest that Increasing the n-Alkane Chain Length Affects the Water/n-Alkane Interfacial Properties in a Manner Similar to that of Cooling

Strong-randomness infinite-coupling phase in a random quantum spin chain

We study the ground-state phase diagram of the Ashkin-Teller random quantum spin chain by means of a generalization of the strong-disorder renormalization group. In addition to the conventional paramagnetic and ferromagnetic (Baxter) phases, we find a partially ordered phase characterized by strong randomness and infinite coupling between the colors. This unusual phase acts, at the same time, as a Griffiths phase for two distinct quantum phase transitions both of which are of infinite-randomness type. We also investigate the quantum multi-critical point that separates the two-phase and three-phase regions; and we discuss generalizations of our results to higher dimensions and other systems.Comment: 9 pages, 6 eps figures, final version as publishe

Infinite-randomness criticality in a randomly layered Heisenberg magnet

We study the ferromagnetic phase transition in a randomly layered Heisenberg magnet using large-scale Monte-Carlo simulations. Our results provide numerical evidence for the infinite-randomness scenario recently predicted within a {strong-disorder renormalization group approach}. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. We also study the perpendicular and parallel spin-wave stiffnesses in the Griffiths phase. In agreement with the theoretical predictions, the parallel stiffness is nonzero for all temperatures $T<T_c$. In contrast, the perpendicular stiffness remains zero in part of the ordered phase, giving rise to anomalous elasticity. In addition, we calculate the in-plane correlation length which diverges already inside the disordered phase at a temperature significantly higher than $T_c$. The time autocorrelation function within model $A$ dynamics displays an ultraslow logarithmic decay at criticality and a nonuniversal power-law in the Griffiths phase.Comment: 8 pages, 8 figures, final version as publishe

Anomalous elasticity in a disordered layered XY model

We investigate the effects of layered quenched disorder on the behavior of planar magnets, superfluids, and superconductors by performing large-scale Monte-Carlo simulations of a three-dimensional randomly layered XY model. Our data provide numerical evidence for the recently predicted anomalously elastic (sliding) intermediate phase between the conventional high-temperature and low-temperature phases. In this intermediate phase, the spin-wave stiffness perpendicular to the layers vanishes in the thermodynamic limit while the stiffness parallel to the layers as well as the spontaneous magnetization are nonzero. In addition, the susceptibility displays unconventional finite-size scaling properties. We compare our Monte-Carlo results with the theoretical predictions, and we discuss possible experiments in ultracold atomic gases, layered superconductors and in nanostructures.Comment: 6 pages, 4 eps figures included, proceedings of FQMT11, final version as publishe

Composition-tuned smeared phase transitions

Phase transitions in random systems are smeared if individual spatial regions can order independently of the bulk system. In this paper, we study such smeared phase transitions (both classical and quantum) in substitutional alloys A$_{1-x}$B$_x$ that can be tuned from an ordered phase at composition $x=0$ to a disordered phase at $x=1$. We show that the ordered phase develops a pronounced tail that extends over all compositions $x<1$. Using optimal fluctuation theory, we derive the composition dependence of the order parameter and other quantities in the tail of the smeared phase transition. We also compare our results to computer simulations of a toy model, and we discuss experiments.Comment: 6 pages, 4 eps figures included, final version as publishe