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

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

Concepts for design of an energy management system incorporating dispersed storage and generation

New forms of generation based on renewable resources must be managed as part of existing power systems in order to be utilized with maximum effectiveness. Many of these generators are by their very nature dispersed or small, so that they will be connected to the distribution part of the power system. This situation poses new questions of control and protection, and the intermittent nature of some of the energy sources poses problems of scheduling and dispatch. Under the assumption that the general objectives of energy management will remain unchanged, the impact of dispersed storage and generation on some of the specific functions of power system control and its hardware are discussed

Scaling in the vicinity of the four-state Potts fixed point

We study a self-dual generalization of the Baxter-Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter-Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.Comment: 19 pages, 7 figure

Surface and bulk transitions in three-dimensional O(n) models

Using Monte Carlo methods and finite-size scaling, we investigate surface criticality in the O$(n)$ models on the simple-cubic lattice with $n=1$, 2, and 3, i.e. the Ising, XY, and Heisenberg models. For the critical couplings we find $K_{\rm c}(n=2)=0.454 1655 (10)$ and $K_{\rm c}(n=3)= 0.693 002 (2)$. We simulate the three models with open surfaces and determine the surface magnetic exponents at the ordinary transition to be $y_{h1}^{\rm (o)}=0.7374 (15)$, $0.781 (2)$, and $0.813 (2)$ for $n=1$, 2, and 3, respectively. Then we vary the surface coupling $K_1$ and locate the so-called special transition at $\kappa_{\rm c} (n=1)=0.50214 (8)$ and $\kappa_{\rm c} (n=2)=0.6222 (3)$, where $\kappa=K_1/K-1$. The corresponding surface thermal and magnetic exponents are $y_{t1}^{\rm (s)} =0.715 (1)$ and $y_{h1}^{\rm (s)} =1.636 (1)$ for the Ising model, and $y_{t1}^{\rm (s)} =0.608 (4)$ and$y_{h1}^{\rm (s)} =1.675 (1)$ for the XY model. Finite-size corrections with an exponent close to -1/2 occur for both models. Also for the Heisenberg model we find substantial evidence for the existence of a special surface transition.Comment: TeX paper and 10 eps figure

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

Monte Carlo Calculation of Free Energy, Critical Point, and Surface Critical Behavior of Three-Dimensional Heisenberg Ferromagnets

A transfer-matrix Monte Carlo technique is developed to compute the free energy of three-dimensional, classical Heisenberg ferromagnets. From the free energy of systems with periodic and antiperiodic boundary conditions, helicity moduli are calculated. From these the critical couplings for simple-cubic (sc) and face-centered-cubic lattices are estimated by use of finite-size scaling. For the simple-cubic lattice, the critical dimension of the surface magnetization is estimated with standard Monte Carlo methods, yielding a result in excellent agreement with the ε-expansion work of Diehl and Nüsser

Gap of the Linear Spin-1 Heisenberg Antiferromagnet: A Monte Carlo Calculation

We have performed Monte Carlo calculations of the energies of several low-lying energy states of one-dimensional, spin-1 Heisenberg antiferromagnets with linear sizes up to n=32. Our results support Haldane’s prediction that a gap exists in the excitation spectrum for n→∞. .A

Affective adaptation = effective transformation? Shifting the politics of climate change adaptation and transformation from the status quo

Alarming rates of environmental change have catalyzed scholars to call for fundamental transformations in social-political and economic relations. Yet cautionary tales about how power and politics are constitutive of these efforts fill the literature. We show how a relational framing of adaptation and transformation demands a political, cross-scalar, and socionatural analysis to probe the affects and effects of climate change and better grasp how transformative change unfolds. We bring affect theory into conversation with the literature on adaptation politics, socio-environmental transformations, subjectivity, and our empirical work to frame our analysis around three under investigated aspects of transformation: (i) the uncertain and unpredictable relations that constitute socionatures; (ii) other ways of knowing; and (iii) the affective and emotional relations that form a basis for action. Affective adaptation represents a different ontological take on transformation by reframing the socionatural, normative and ethical aspects as relational, uncertain, and performative. This directs analytical attention to processes rather than outcomes. The emphasis on the encounter between bodies in affect theory points to the need for experiential and embodied ways of knowing climate to effect transformative change. Effective transformation requires recognizing uncertainty and unpredictability as part of transformative processes. This is not because all outcomes are acceptable, but rather because uncertainty and unpredictability are elements which help generate affects (action) and emotional commitment to shared human and more than human relations in action, projects, and policies. This article is categorized under: Vulnerability and Adaptation to Climate Change > Values-Based Approach to Vulnerability and Adaptatio