Paradigm For Phase Transitions Research Articles

Probing XY phase transitions in a Josephson junction array with tunable frustration

The seminal theoretical works of Berezinskii, Kosterlitz, and Thouless presented a new paradigm for phase transitions in condensed matter that are driven by topological excitations. These transitions have been extensively studied in the context of two-dimensional XY models -- coupled compasses -- and have generated interest in the context of quantum simulation. Here, we use a circuit quantum-electrodynamics architecture to study the critical behavior of engineered XY models through their dynamical response. In particular, we examine not only the unfrustrated case but also the fully-frustrated case which leads to enhanced degeneracy associated with the spin rotational [U$(1)$] and discrete chiral ($Z_2$) symmetries. The nature of the transition in the frustrated case has posed a challenge for theoretical studies while direct experimental probes remain elusive. Here we identify the transition temperatures for both the unfrustrated and fully-frustrated XY models by probing a Josephson junction array close to equilibrium using weak microwave excitations and measuring the temperature dependence of the effective damping obtained from the complex reflection coefficient. We argue that our probing technique is primarily sensitive to the dynamics of the U$(1)$ part.

Unconventional phase transitions in liquid crystals

According to classical textbooks on thermodynamics or statistical physics, there are only two types of phase transitions: continuous, or second-order, in which the latent heat L is zero, and first-order, in which L ≠ 0. Present-day textbooks and monographs also mention another, stand-alone type—the Berezinskii–Kosterlitz–Thouless transition, which exists only in two dimensions and shares some features with first- and second-order phase transitions. We discuss examples of non-conventional thermodynamic behavior (i.e., which is inconsistent with the theoretical phase transition paradigm now universally accepted). For phase transitions in smectic liquid crystals, mechanisms for nonconventional behavior are proposed and the predictions they imply are examined.

Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model.

Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of systems near critical points. These universal properties make it possible to estimate how far a system is from a critical threshold. Several early-warning signals have been reported in time series representing systems near catastrophic shifts. The proper understanding of these early-warnings may allow the prediction and perhaps control of these dramatic shifts in a wide variety of systems. In this paper we analyze this universal behavior for a system that is a paradigm of phase transitions, the Ising model. We study the behavior of the early-warning signals and the way the temporal correlations of the system increase when the system is near the critical point.

SUPERCONDUCTOR-INSULATOR TRANSITIONS

Superconductor-insulator transitions, especially in thin films, can provide the simplest examples of the continuous quantum phase transition paradigm. Quantum phase transitions differ from thermal phase transitions in that they occur at zero temperature when the ground state of a system is changed in response to a variation of an external parameter of the Hamiltonian. In the example of the superconductor-insulator transition, this control parameter could be the parallel or perpendicular magnetic field, disorder, or charge density. Quantum phase transitions are studied through measurements at nonzero temperature of physical behaviors influenced by the quantum fluctuations associated with the transition. This review will focus on experimental aspects of superconductor-insulator transition in disordered films that are effectively two-dimensional. In particular, the evidence for quantum critical behavior in the various types of transitions will be presented. The various theoretical scenarios for the transitions will also be discussed along with the extent to which they are supported by experiment. Open questions relating to the nature of the very puzzling insulating regime and whether there are many different types of superconductor-insulator transitions will be presented. Although this research area is more than 20 years old, rather central issues are not resolved.

A Dynamic Systems Approach to the Effects of Aging on Bimanual Coordination

The present study examined the effects of aging on the execution of a bimanual coordination task in a classical phase transition paradigm in which coordination patterns (in-phase and anti-phase) and movement frequency were manipulated. Two groups of adults, the so-called young (average age 26 years) and old (average age 71 years) participants, performed both in-phase and anti-phase patterns at different frequencies. As we expected variability of relative phase was larger for older participants than for younger ones for both the in-phase and the anti-phase coordination patterns. Moreover, phase transitions occurred at lower frequencies for older participants and more transitions were observed for older than for younger participants. Although no specific hypotheses were made about the prominent source(s) of age-related changes in coordination dynamics (i.e., an alteration in the coupling function and/or an increase of the magnitude of noise), our results suggest that these changes might result from increases in the (neural) noise to be found in the (bimanual) action system.

Intentional and attentional dynamics of speech–hand coordination

Interest is rapidly growing in the hypothesis that natural language emerged from a more primitive set of linguistic acts based primarily on manual activity and hand gestures. Increasingly, researchers are investigating how hemispheric asymmetries are related to attentional and manual asymmetries (i.e., handedness). Both speech perception and production have origins in the dynamical generative movements of the vocal tract known as articulatory gestures. Thus, the notion of a “gesture” can be extended to both hand movements and speech articulation. The generative actions of the hands and vocal tract can therefore provide a basis for the (direct) perception of linguistic acts. Such gestures are best described using the methods of dynamical systems analysis since both perception and production can be described using the same commensurate language. Experiments were conducted using a phase transition paradigm to examine the coordination of speech–hand gestures in both left- and right-handed individuals. Results address coordination (in-phase vs. anti-phase), hand (left vs. right), lateralization (left vs. right hemisphere), focus of attention (speech vs. tapping), and how dynamical constraints provide a foundation for human communicative acts. Predictions from the asymmetric HKB equation confirm the attentional basis of functional asymmetry. Of significance is a new understanding of the role of perceived synchrony (p-centres) during intentional cases of gestural coordination.