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

Transfer-Matrix Monte Carlo Estimates of Critical Points in the Simple Cubic Ising, Planar and Heisenberg Models

The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the statistical noise can be reduced considerably by a similarity transformation of the transfer matrix using a variational estimate of its leading eigenvector, in analogy with a common practice in various quantum Monte Carlo techniques. Here we take the two-dimensional coupled $XY$-Ising model as an example. Furthermore, we calculate interface free energies of finite three-dimensional O($n$) models, for the three cases $n=1$, 2 and 3. Application of finite-size scaling to the numerical results yields estimates of the critical points of these three models. The statistical precision of the estimates is satisfactory for the modest amount of computer time spent

Decoupling in the 1D frustrated quantum XY model and Josephson junction ladders: Ising critical behavior

A generalization of the one-dimensional frustrated quantum XY model is considered in which the inter and intra-chain coupling constants of the two infinite XY (planar rotor) chains have different strengths. The model can describe the superconductor to insulator transition due to charging effects in a ladder of Josephson junctions in a magnetic field with half a flux quantum per plaquette. From a fluctuation-effective action, this transition is expected to be in the universality class of the two-dimensional classical XY-Ising model. The critical behavior is studied using a Monte Carlo transfer matrix applied to the path-integral representation of the model and a finite-size-scaling analysis of data on small system sizes. It is found that, unlike the previous studied case of equal inter and intra-chain coupling constants, the XY and Ising-like excitations of the quantum model decouple for large interchain coupling, giving rise to pure Ising model critical behavior for the chirality order parameter and a superconductor-insulator transition in the universality class of the 2D classical XY model.Comment: 15 pages with figures, RevTex 3.0, INPE-93/00

Forming norms: informing diagnosis and management in sports medicine

Clinicians aim to identify abnormalities, and distinguish harmful from harmless abnormalities. In sports medicine, measures of physical function such as strength, balance and joint flexibility are used as diagnostic tools to identify causes of pain and disability and monitor progression in response to an intervention. Comparing results from clinical measures against ‘normal’ values guides decision-making regarding health outcomes. Understanding ‘normal’ is therefore central to appropriate management of disease and disability. However, ‘normal’ is difficult to clarify and definitions are dependent on context. ‘Normal’ in the clinical setting is best understood as an appropriate state of physical function. Particularly as disease, pain and sickness are expected occurrences of being human, understanding ‘normal’ at each stage of the lifespan is essential to avoid the medicalisation of usual life processes. Clinicians use physical measures to assess physical function and identify disability. Accurate diagnosis hinges on access to ‘normal’ reference values for such measures. However our knowledge of ‘normal’ for many clinical measures in sports medicine is limited. Improved knowledge of normal physical function across the lifespan will assist greatly in the diagnosis and management of pain, disease and disability

Numerical Studies of the Two Dimensional XY Model with Symmetry Breaking Fields

We present results of numerical studies of the two dimensional XY model with four and eight fold symmetry breaking fields. This model has recently been shown to describe hydrogen induced reconstruction on the W(100) surface. Based on mean-field and renormalization group arguments,we first show how the interplay between the anisotropy fields can give rise to different phase transitions in the model. When the fields are compatible with each other there is a continuous phase transition when the fourth order field is varied from negative to positive values. This transition becomes discontinuous at low temperatures. These two regimes are separated by a multicritical point. In the case of competing four and eight fold fields, the first order transition at low temperatures opens up into two Ising transitions. We then use numerical methods to accurately locate the position of the multicritical point, and to verify the nature of the transitions. The different techniques used include Monte Carlo histogram methods combined with finite size scaling analysis, the real space Monte Carlo Renormalization Group method, and the Monte Carlo Transfer Matrix method. Our numerical results are in good agreement with the theoretical arguments.Comment: 29 pages, HU-TFT-94-36, to appear in Phys. Rev. B, Vol 50, November 1, 1994. A LaTeX file with no figure

Conformal Anomaly and Critical Exponents of the XY-Ising Model

We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional $XY$-Ising model. This model is expected to describe the critical behavior of a class of systems with simultaneous $U(1)$ and $Z_2$ symmetries of which the fully frustrated $XY$ model is a special case. The effective values obtained for $c$ show a significant decrease with $L$ at different points along the line where the transition to the ordered phase takes place in a single transition. Extrapolations based on power-law corrections give values consistent with $c=3/2$ although larger values can not be ruled out. Critical exponents are obtained more accurately and are consistent with previous Monte Carlo simulations suggesting new critical behavior and with recent calculations for the frustrated $XY$ model.Comment: 33 pages, 13 latex figures, uses RevTeX 3.

'Voices in Frickley' : the struggles of the miners at a Yorkshire colliery 1984-1993

In this study the author focuses on the activities of the National Uniol1" of Mineworkers at Frickley Colliery during ten years of industrial conflict prior to the pit's closure in November 1993. While the initial part of this period, the 1984-85 miners' strike, has been well documented by scholars, the conflict in the following years has received scant attention. Following the miners' defeat, the NUM members at Frickley played an important part in sustaining the tradition of militant trade unionism in the Yorkshire coalfield at a time of general retreat for the British labour movement. Other studies have concentrated mainly on the activities of union leaders and management figures when chronicling the confrontation in the coalfields. In contrast, a substantial part of the present author's account is based on the oral testimonies of pit level activists, thus aspects of the conflict that have been otherwise ignored or overlooked are brought to light. At the core of the study is the contention that the labour movement had become disabled by the defeatist notion of 'new realism'. Moreover, it is illustrated how the NUM leadership in Yorkshire, conventionally portrayed as being militant, was often instrumental in suffocating the resistance of the NUM rank and file as they challenged the authoritarian working practices being imposed by the management of the industry

Conformal invariance and linear defects in the two-dimensional Ising model

Using conformal invariance, we show that the non-universal exponent eta_0 associated with the decay of correlations along a defect line of modified bonds in the square-lattice Ising model is related to the amplitude A_0=xi_n/n of the correlation length \xi_n(K_c) at the bulk critical coupling K_c, on a strip with width n, periodic boundary conditions and two equidistant defect lines along the strip, through A_0=(\pi\eta_0)^{-1}.Comment: Old paper, for archiving. 5 pages, 4 figures, IOP macro, eps

Improved Phenomenological Renormalization Schemes

An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made using two-dimensional Ising and Potts lattices and the three-dimensional Ising model. Variants of equations for the phenomenological renormalization group are obtained which ensure more rapid convergence than the conventionally used Nightingale phenomenological renormalization scheme. An estimate is obtained for the critical finite-size scaling amplitude of the internal energy in the three-dimensional Ising model. It is shown that the two-dimensional Ising and Potts models contain no finite-size corrections to the internal energy so that the positions of the critical points for these models can be determined exactly from solutions for strips of finite width. It is also found that for the two-dimensional Ising model the scaling finite-size equation for the derivative of the inverse correlation length with respect to temperature gives the exact value of the thermal critical exponent.Comment: 14 pages with 1 figure in late

A Logical Approach to Real Options Identification with Application to UAV Systems

Complex systems are subject to uncertainties that may lead to suboptimal performance or even catastrophic failure if unmanaged. Uncertainties may be managed through real options that provide a decision maker with the right, but not the obligation, to exercise actions in the future. While real options analysis has traditionally been used to quantify the value of such flexibility, this paper is motivated by the need for a structured approach to identify where real options are or can be embedded for uncertainty management. We introduce a logical model-based approach to identification of real option mechanisms and types, where the mechanism is the enabler of the option, while the type refers to the flexibility provided by the option. First, we extend the classical design structure matrix and the more general multiple-domain matrix (MDM), commonly used in modeling and analyzing interdependencies in complex socio-technical systems, to the more expressive Logical-MDM that supports the representation of flexibility. Second, we show that, in addition to flexibility, two new properties, namely, optionability and realizability, are relevant to the identification of real options. We use the Logical-MDM to estimate flexibility, optionability, and realizability metrics. Finally, we introduce the Real Options Identification (ROI) method based on these metrics, where the identified options are valued using standard real options valuation methods to support decision making under uncertainty. The expressivity of the logic combined with the structure of the dependency model allows the effective representation and identification of mechanisms and types of real options across multiple domains and lifecycle phases of a system. We demonstrate this approach through a series of unmanned air vehicle scenarios