Compass Model Research Articles

Quantum phase transition in the quantum compass model

In this work, we show that the quantum compass model on a square lattice can be mapped to a fermionic model with local-density interaction. We introduce a mean-field approximation where the most important fluctuations, those perpendicular to the ordering direction, are taken into account exactly. It is found that the quantum phase transition point at ${J}_{x}={J}_{z}$ marks a first-order phase transition. We also show that the mean-field result is robust against the remaining fluctuation corrections up to the second order.

PBL in the Undergraduate MD Program at McMaster University: Three Iterations in Three Decades

When the undergraduate MD program of McMaster University admitted its first cohort of 20 students in 1969, it heralded a major change in medical school pedagogy that has influenced the education of medical students around the world. The three-year PBL curriculum, which emphasized small-group tutorials, self-directed learning, a minimal number of didactic presentations, and student evaluation that was based almost entirely on performance in the tutorial, represented a radical departure from traditional curricula. Since the inception of the original curriculum in 1969, there have been two major curriculum revisions, the most recent of which was in 2005. The original curriculum attempted to integrate both basic science and clinical science into the biomedical problems. The second iteration of the curriculum focused on priority health problems and centered on a list of common medical problems as the foundation for curriculum organization, on the basis that an understanding of the management of common conditions included areas of knowledge that would be essential for clinical competence. Under the third, current curriculum, the COMPASS (concept-oriented, multidisciplinary, problem-based, practice for transfer, simulations in clerkship, streaming) model was adopted. Under this concept-based system, emphasis is placed on underscoring the underlying concepts in the curriculum with a logical sequencing of both the concepts and the body systems. This article briefly reviews the history of the development of the undergraduate MD program at McMaster and the three curricula that have been developed during the past three decades.

Dilution effects on orbital order in strongly correlated electron systems

Dilution effects in orbital ordered systems with strong electron correlation are studied theoretically. Vacancy-concentration x dependence of the orbital-ordering temperature T OO calculated in the two-representative orbital models, i.e. the e g-orbital model in a three dimensional square lattice and the two-dimensional orbital compass model. Reduction of T OO as a function of x is stronger than that in dilute magnets and is not explained by the simple percolation theory. This phenomenon is attributed to the directional interaction between orbitals. It is shown that due to the quantum effects, the effective dimensionality in the system is increased and the orbital order becomes robust against dilution. The present calculation provides a new aspect of the dilute ordered state in strongly correlated electron systems.

Dilution effects in classical and quantum orbital systems

We examine the dilution effects in an orbital model, termed the orbital compass model, which corresponds to the two-dimensional version of the e g -orbital model. An unconventional low-dimensional orbital alignment termed the directional order is confirmed to be realized by utilizing the quantum Monte-Carlo method. Impurity dependence of the ordering temperature of the directional order is numerically examined. We show that the quantum effect makes the directional order robust against doping of impurities.

The Lambda Method for the GNSS Compass

The Lambda Method for the GNSS CompassGlobal Navigation Satellite System carrier phase ambiguity resolution is the key to high precision positioning and attitude determination. In this contribution we consider the GNSS compass model. We derive the integer least-squares estimators and discuss the various steps involved in the ambiguity resolution process. This includes the method that has successfully been used in (Park and Teunissen, 2003). We emphasize the unaided, single frequency, single epoch case, since this is considered the most challenging mode of GNSS attitude determination.

Quantum compass model on the square lattice

Using exact diagonalizations, Green's function Monte Carlo simulations and high-order perturbation theory, we study the low-energy properties of the two-dimensional spin-1/2 compass model on the square lattice defined by the Hamiltonian $H = - \sum_{\bm{r}} (J_x \sigma_{\bm{r}}^x \sigma_{\bm{r} + \bm{e}_x}^x + J_z \sigma_{\bm{r}}^z \sigma_{\bm{r} + \bm{e}_z}^z)$. When $J_x\ne J_z$, we show that, on clusters of dimension $L\times L$, the low-energy spectrum consists of $2^L$ states which collapse onto each other exponentially fast with $L$, a conclusion that remains true arbitrarily close to $J_x=J_z$. At that point, we show that an even larger number of states collapse exponentially fast with $L$ onto the ground state, and we present numerical evidence that this number is precisely $2\times 2^L$. We also extend the symmetry analysis of the model to arbitrary spins and show that the two-fold degeneracy of all eigenstates remains true for arbitrary half-integer spins but does not apply to integer spins, in which cases eigenstates are generically non degenerate, a result confirmed by exact diagonalizations in the spin-1 case. Implications for Mott insulators and Josephson junction arrays are briefly discussed.

Discrete sliding symmetries, dualities, and self-dualities of quantum orbital compass models andp+ipsuperconducting arrays

We study the spin-$1∕2$ two- and three-dimensional orbital compass models relevant to the problem of orbital ordering in transition metal oxides. We show that these systems display self-dualities and gauge-like discrete sliding symmetries. An important and surprising consequence is that these models are dual to (seemingly unrelated) recently studied models of $p+ip$ superconducting arrays. The duality transformations are constructed by means of a path-integral representation in discretized imaginary time and considering its ${\mathbb{Z}}_{2}$ spatial reflection symmetries and space-time discrete rotations, we obtain, in a transparent unified geometrical way, several dualities. We also introduce an alternative construction of the duality transformations using operator identities. We discuss the consequences of these dualities for the order parameters and phase transitions of the orbital compass model and its generalizations, and apply these ideas to a number of related systems.

Orbital-only models: ordering and excitations

We consider orbital-only models in Mott insulators, where the orbital–orbital interactions are either due to Jahn–Teller distortions or due to the Kugel–Khomskii superexchange. This leads to highly anisotropic and frustrated orbital Hamiltonians. For two-fold degenerate eg systems, both types of orbital interactions lead to the same form of the Hamiltonian—the 120° model. In both cases, the predicted symmetry of the orbital ordering is the same, although different from the one observed experimentally. The orbital operators that appear in the two kinds of orbital-only Hamiltonians are different. In the case of superexchange, the orbital degrees of freedom are represented by quantum pseudo-spin 1/2 operators. But when the interactions are Jahn–Teller mediated and the coupling with the lattice is strong, the orbital operators are essentially classical pseudospins. Thus as a function of the relative coupling strengths, a quantum-to-classical crossover is expected. For three-fold degenerate t2g orbitals, the Jahn–Teller coupling gives rise to a particular type of orbital compass models. We point out that fluctuations—whether due to quantum effects or finite temperature—are of prime importance for ordering in the 120° and orbital compass models. The fluctuations generally generate a gap in the orbital excitation spectrum. These orbital excitations—orbitons—are hybrid excitations that carry both a lattice Jahn–Teller and a magnetic Kugel–Khomskii character.

Directional Ordering of Fluctuations in a Two-Dimensional Compass Model

In the Mott insulating phase of the transition metal oxides, the effective orbital-orbital interaction is directional both in orbital space and in real space. We discuss a classical realization of directional coupling in two dimensions. Despite extensive degeneracy of the ground state, the model exhibits partial orbital ordering in the form of directional ordering of fluctuations at low temperatures stabilized by an entropy gap. Transition to the disordered phase is shown to be in the Ising universality class through exact mapping and multicanonical Monte Carlo simulations.

Religious interpretations of suffering by parents of a child with spina bifida

= 0.66), apathy (M = 1.7, SD = 0.73), lament (M = 1.9, SD = 0.87), plan (M = 2.3, SD = 1.14) and doubt the compassion model, though also with an inclination towards rejection (M = 2.6, SD = 1.22). In answer to the second question significant variations of the means are found for the models of retribution (eta = 0.34), compassion (eta = 0.57) and plan (eta = 0.40) that indicate a far stronger support of the aforementioned models when church involvement increases, leading for instance to positive support of the compassion model of theodicy. Conclusion Interpretations of the scores on theodicy will be discussed.

A refined view of the determinants of gait.

We evaluated the effect of reducing the vertical displacement of the centre of mass (COM) on the six determinants of gait proposed by Saunders, Inman and Eberhart in 30 healthy adults. We compared the estimated reduction in COM vertical displacement due to the determinants in their compass model with the actual reduction of vertical displacement. The maximum height of the COM for the compass gait model occurred earlier than the actual COM maximum height. Different gait functions were determinant in reducing COM vertical displacement. In both cases heel rise was the main determinant (up to 2/3 of total reduction). Pelvic obliquity and single stance knee flexion contributions were more important when compass gait COM maximum was used while they were barely detectable at the actual COM maximum. Ipsi- and contra-lateral knee flexion were detrimental to the reduction of COM vertical displacements, while pelvic rotation contribution was beneficial and accounted for up to 10% of the overall COM vertical displacement reduction. Although a reduction of COM vertical displacement may have important energy implications, determining the specific gait parameters associated with this function is fundamental in understanding gait disability.

A refined view of the determinants of gait: Significance of heel rise

Kerrigan DC, Della Croce U, Marciello M, Riley PO. A refined view of the determinants of gait: significance of heel rise. Arch Phys Med Rehabil 2000;81:1077-80. Objectives: Although the major determinants of gait described by Saunders and colleagues have been accepted for more than 40 years, recent investigations raise the question of whether the reduction in center of mass (COM) displacement compared with a compass gait model indeed results from the factors originally described. We tested the hypothesis that heel rise at the end of stance is a true determinant that can explain a considerable portion of the reduction in COM vertical displacement during walking. Design: Stereophotogrammetric data during walking were collected. A modified compass gait model incorporating the effect of heel rise, as compared with predictions based on a standard compass model, were used to estimate the isolated effect of heel rise on reducing the vertical displacement of COM. Setting: A gait laboratory. Participants: Thirty able-bodied subjects. Main Outcome Measure: The estimated reduction in COM displacement due to heel rise was compared with the actual reduction in displacement. Results: The estimated effect of heel rise on reduction in COM displacement was 23.4 ± 7.6mm, whereas the actual reduction in COM displacement was 21.2 ± 6.5mm (difference not significant, paired p = .185). Conclusion: During normal walking, heel rise from foot flat has a considerable role in raising the height of the COM when it is at its lowest, thus reducing its overall displacement. Insofar as reduction of COM vertical displacement may have important energy implications, appreciating the specific gait parameter of heel rise is key in rehabilitative approaches to improve gait disability. © 2000 by the American Congress of Rehabilitation Medicine and the American Academy of Physical Medicine and Rehabilitation

Improving Health Care, Part 5: Applying the Dartmouth Clinical Improvement Model to Community Health

Traditional approaches to community health initiatives provide guidance on community mobilization, health assessment, planning, and intervention. Yet direction in how to frame the action steps to implement and measure results is often missing. Many community health initiatives find implementation overwhelming and ineffectual. FRAMEWORK FOR COMMUNITY HEALTH-THE CLINICAL IMPROVEMENT MODEL: The process--outcome methodology of continuous quality improvement (CQI) can translate large community aims into manageable projects. The sequential application of the clinical improvement model and the Community Health Value Compass for measuring outcomes-in state of health, quality of life, satisfaction, and costs-provides a link between data and action, thereby producing accountability for the community health initiative. USING THE CLINICAL IMPROVEMENT MODEL IN TWIN FALLS: Healthy Magic Valley (Twin Falls, Idaho) is the vision for long-term improvement in health status and reduction of health risks for the Southcentral Idaho Health Network. Since 1996 the Twin Falls Community Health Collaborative and SAFE KIDS Coalition have used the Value Compass model and CQI methods to decrease the rate of motor vehicle collisions, serious injuries, and deaths involving teens, while reducing the health, educational, legal, and financial consequences associated with teen-involved motor vehicle collisions. In 1993 the Twin Falls collaborative convened to apply CQI methods to the health of the community. The team has since met periodically to address the issues of community health, using the Dartmouth value compass model since 1996. Each sequential application of the process-outcome CQI framework exposes a blueprint for action and the unfolding of a health improvement strategy. The interventions should affect one or more dimensions of the value compass for teenage driving and motor vehicle collisions. CASE STUDY OF THE CLINICAL IMPROVEMENT MODEL: The motor vehicle death in October 1997 of a high school football player, who was not wearing a seat belt, led to a call to action for injury prevention. Implementation of a local community health initiative on seat belt use started in 1998. A strategy was developed to address implementation of the project among high school teens (for immediate impact) and elementary school children (for long-term impact) and to promote collaboration between the school and the rest of the community. Observed use of seat belts increased from January to September 1998. Data on fatality rates; injury rates; percentages of teens in crashes, of teens injured, and of teen collisions involving use of alcohol; and comprehensive costs are also monitored. Once coalitions are built and priorities set, the Dartmouth clinical improvement model presents a method that emphasizes measuring the benefits to the individual members of the community. A portfolio composed of a value compass for each health improvement initiative provides ongoing feedback for guiding subsequent strategic planning by the governing community health network.

Collaborative Observation: Putting Classroom Instruction at the Center of School Reform

Collaborative Observation: Putting Classroom Instruction at the Center of School Reform, by Karen H. Peters and Judith K. March. Thousand Oaks, Ca: Corwin Press, 1997. 144 pp. $18.95 /cloth. Reviewed by Marian White-Hood, Prince George's County (MD) Public Schools. The fundamental purpose of Collaborative Observation: Putting Classroom Instruction at the Center of School Reform is to show how collaborative observation can be used as an influential strategy for school reform. Additionally, it helps readers gain the necessary perspectives with which to debate urgent issues concerning classroom instruction and school reform. As the book unfolds, one senses the passion, and conviction of authors Peters and March in communicating their viewpoint. Indeed, their credentials are reputable, and their book is credible. Peters is assistant director of the Center for Educational Leadership Services and the Ohio Satellite for Effective Schools at Kent State University, while March serves as the director of the Center. Both have had school system experience and have expertise in curriculum design, clinical supervision, strategic planning for school-based decision making, and staff development. The authors commence by making a poignant distinction between successful and unsuccessful reform initiatives. They argue that four notions undergird successful reform: (a) changes in classroom instruction, (b) districtwide commitment, (c) the quality of professional development programming anchored by the initiative, and (d) a collaborative observation process that allows for peer assistance, feedback, and planning. These four points serve as the catalysts for the creation of their COMPASS model, a collaborative process and metaphor for finding oneself as a teacher, setting a direction, following a course by observing significant signs, and noting transformations of the teacher and observer which leads to student achievement. Four powerful steps regulate this model: a pre-observation conference, in-class data collection and analysis, a post-observation conference, and the development of a collaborative action plan. In simple, clearly written prose, Peters and March introduce the COMPASS model. Their work builds upon adult learning theories while supporting the growth of teachers, observers, and students. Each chapter takes readers through a step in the model's program. In chapter two, Collecting Data: Prior to and During Classroom Observation, the authors contrast their method of data collection with others described in the school reform literature. They also present the format for the pre-observation conference and outline the skills needed by both observer and teacher. Several pre-observation conference forms reflecting best practices research and connections to experiential learning theory are provided. The chapter further explains how the observer and teacher, working as partners, should discuss unit objectives, motivation, and the integration of the lesson. Clarifying questions, which extend and refine the teachers' thinking about the lesson, are also provided. Peters and March also present scripting as a major skill to be learned by observers as part of the in-class data collection process. Readers learn how script pages coupled with classroom diagrams become the springboard for further dialogue and for building academic trust between partners. Chapter three is devoted to the post-observation conference. It outlines the data analysis steps and is rich with examples of analysis statements, scenarios, and techniques. The power of the post-observation conference is illuminated as the authors describe its two phases: planning and delivery. If readers desire additional information, research notes on the lesson analysis and post-observation conference are found at the conclusion of the chapter. Chapter four covers the development of the collaborative action plan and is the most critical chapter of the book. …

Learning Theodicy

AbstractThis article focuses on the problem of theodicy as a subject-matter for religious education. The question is raised whether it is possible to gain comprehension of theodicy models and, if so, to what extent. Empirical research on the effects of a theodicy course, dealing with the retaliation model, the plan model and the compassion model, shows that it indeed is possible to 'learn' theodicy models. Furthermore, our results also show that students especially gain comprehension of the plan model; a theodicy model which explains human suffering from a teleological point of view. Although both the plan model as well as the retaliation model nowadays do not find theological favour, we still consider these results of great value. With regard to the theodicy issue, our course, apparently, enables students to develop their own religious frame of reference in a competent and independent way.

Being a Christian in the Business World: The Challenge and the Promise

What does it mean to be a Christian in today's business world? It is this question which provides the focus for a course I teach called “Modern Decision Making in the Christian Tradition.” The course is designed for college juniors and seniors who are interested in exploring the implications of Christian faith for a professional life. Students are exposed to the flaws in Adam Smith's famous apology for the capitalist economy and offered an approach to working in the system and reforming it from a Christian standpoint.It has been my experience that most students in the course are serious about their Christian faith, that is, they go to church on Sunday and they strive to live the sort of life that they understand to be Christian. They are largely from good homes and have learned the value of friendship and love from dedicated parents. Most of them, however, have not been challenged to think through the implications of their Christian faith for their life in the business world or in the wider social order.While they may be models of compassion and generosity to those in their immediate circles, many students today have a blindspot for responsibilities in the socio-political order. In the traditional vocabulary, they are strong on charity but weak in justice. Justice in our time is often equated with “law and order,” the quid pro quo's that insure that we each get what we deserve. One of the objectives of the course is to widen the horizons of the students so that they come to see more adequately what is entailed in calling oneself “Christian.” To begin, I have them reflect on sections of “Justice in the World,” the document issued by the Roman Synod of Bishops in 1971.

Initial orientation of homing pigeons at the magnetic equator with and without sun compass

To test the present hypotheses concerning the functioning of the bird's magnetic compass, pigeons reared near the magnetic and geographic equator (Fortaleza, NE Brasil) were released 300 km NW of their home in the horizontal field at the magnetic equator. Pigeons released in the morning and in the afternoon were roughly homeward oriented whereas pigeons released at noon with the sun near the zenith vanished close to magnetic north. According to the Wiltschko model of the magnetic compass they should not be able to pick up specific directions. A considerable number of young and inexperienced pigeons returned home against a continuously blowing trade wind. This result contradicts the hypothesis of olfactory navigation as currently discussed.