Universal Dynamics of Independent Critical Relaxation Modes

Scaling behavior is studied of several dominant eigenvalues of spectra of Markov matrices and the associated correlation times governing critical slowing down in models in the universality class of the two-dimensional Ising model. A scheme is developed to optimize variational approximants of progressively rapid, independent relaxation modes. These approximants are used to reduce the variance of results obtained by means of an adaptation of a quantum Monte Carlo method to compute eigenvalues subject to errors predominantly of statistical nature. The resulting spectra and correlation times are found to be universal up to a single, non-universal time scale for each model

Excitation Spectrum at the Yang-Lee Edge Singularity of 2D Ising Model on the Strip

At the Yang-Lee edge singularity, finite-size scaling behavior is used to measure the low-lying excitation spectrum of the Ising quantum spin chain for free boundary conditions. The measured spectrum is used to identify the CFT that describes the Yang-Lee edge singularity of the 2D Ising model for free boundary conditions.Comment: 7 pages, 1 figur

Critical Excitation Spectrum of Quantum Chain With A Local 3-Spin Coupling

This article reports a measurement of the low-energy excitation spectrum along the critical line for a quantum spin chain having a local interaction between three Ising spins and longitudinal and transverse magnetic fields. The measured excitation spectrum agrees with that predicted by the (D$_4$, A$_4$) conformal minimal model under a nontrivial correspondence between translations at the critical line and discrete lattice translations. Under this correspondence, the measurements confirm a prediction that the critical line of this quantum spin chain and the critical point of the 2D 3-state Potts model are in the same universality class.Comment: 7 pages, 2 figure

Monte Carlo computation of correlation times of independent relaxation modes at criticality

We investigate aspects of universality of Glauber critical dynamics in two dimensions. We compute the critical exponent $z$ and numerically corroborate its universality for three different models in the static Ising universality class and for five independent relaxation modes. We also present evidence for universality of amplitude ratios, which shows that, as far as dynamic behavior is concerned, each model in a given universality class is characterized by a single non-universal metric factor which determines the overall time scale. This paper also discusses in detail the variational and projection methods that are used to compute relaxation times with high accuracy

A qualitative analysis of staff-client interactions within a breast cancer assessment clinic

Objectives Breast screening clients recalled to an assessment clinic experience high levels of anxiety. The culture of the assessment clinic may impact upon client experience, which may influence their future re-engagement in screening. This study aimed to explore the culture of staff-client interactions within a breast cancer assessment clinic. Materials and methods Following an ethnographic approach, twenty-three client journeys were observed, followed by semi-structured interviews with the clients. The observation and interview data were analysed to produce research themes, which were then explored within two focus groups to add a practitioner perspective. Results Multiple staff-client interaction events were observed over a period of several weeks. Client interview feedback was overwhelmingly positive. Three recurrent and sequential themes emerged: breaking down barriers, preparing the ground and sign-posting. These themes outline the changing focus of staff-client interactions during the client's clinic journey, encompassing how anxieties were expressed by clients, and responded to by practitioners. Conclusion This study was the first to explore in depth the staff-client interaction culture within a breast assessment clinic using an ethnographic approach. A new perspective on professional values and behaviours has been demonstrated via a model of staff-client interaction. The model documents the process of guiding the client from initial confusion and distress to an enhanced clarity of understanding. A recommendation most likely to have a positive impact on the client experience is the introduction of a client navigator role to guide the clients through what is often a lengthy, stressful and confusing process

The phase diagram of the anisotropic Spin-1 Heisenberg Chain

We applied the Density Matrix Renormalization Group to the XXZ spin-1 quantum chain. In studing this model we aim to clarify controversials about the point where the massive Haldane phase appears.Comment: 2 pages (standart LaTex), 1 figure (PostScript) uuencode

The Dynamic Exponent of the Two-Dimensional Ising Model and Monte Carlo Computation of the Sub-Dominant Eigenvalue of the Stochastic Matrix

We introduce a novel variance-reducing Monte Carlo algorithm for accurate determination of autocorrelation times. We apply this method to two-dimensional Ising systems with sizes up to $15 \times 15$, using single-spin flip dynamics, random site selection and transition probabilities according to the heat-bath method. From a finite-size scaling analysis of these autocorrelation times, the dynamical critical exponent $z$ is determined as $z=2.1665$ (12)

Learning When to Use Automatic Tabulation in Constraint Model Reformulation

Combinatorial optimisation has numerous practical applications, such as planning, logistics, or circuit design. Problems such as these can be solved by approaches such as Boolean Satisfiability (SAT) or Constraint Programming (CP). Solver performance is affected significantly by the model chosen to represent a given problem, which has led to the study of model reformulation. One such method is tabulation: rewriting the expression of some of the model constraints in terms of a single “table” constraint. Successfully applying this process means identifying expressions amenable to transformation, which has typically been done manually. Recent work introduced an automatic tabulation using a set of hand-designed heuristics to identify constraints to tabulate. However, the performance of these heuristics varies across problem classes and solvers. Recent work has shown learning techniques to be increasingly useful in the context of automatic model reformulation. The goal of this study is to understand whether it is possible to improve the performance of such heuristics, by learning a model to predict whether or not to activate them for a given instance. Experimental results suggest that a random forest classifier is the most robust choice, improving the performance of four different SAT and CP solvers

Finite-size scaling corrections in two-dimensional Ising and Potts ferromagnets

Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width $N$ sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the ``analytical'' correction terms, $N^{-2}$, are identically zero for triangular-- and honeycomb Ising systems. For Potts spins, our results are broadly consistent with this lattice-dependent pattern of cancellations, though for correlation lengths non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out.Comment: 11 pages, LaTeX with Institute of Physics macros, 2 EPS figures; to appear in Journal of Physics

Semistochastic Projector Monte Carlo Method

We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer.Comment: 5 pages, 5 figure