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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 figures

A load-tolerant External Conjugate-T (ECT) impedance matching system for two A2 Ion Cyclotron Resonance Heating (ICRH) antennas has been successfully put into operation at JET. The system allows continuous injection of the RF power into plasma in the presence of strong antenna loading perturbations caused by Edge Localized Modes (ELMs). Reliable ECT performance has been demonstrated under a variety of antenna loading conditions including H-mode plasmas with Radial Outer Gaps (ROG) in the range of 4-14 cm. The high resilience to ELMs predicted during the circuit simulations has been fully confirmed experimentally. Dedicated arc detection techniques and real-time matching algorithms have been developed as a part of the ECT project. The new Advanced Wave Amplitude Comparison System (AWACS) has proven highly efficient in detection of arcs both between and during ELMs. The ECT system has allowed the delivery of up to 4 MW of RF power without trips into plasmas with Type-I ELMs. Together with the 3dB system and the ITER-Like Antenna (ILA), the ECT has brought the total RF power coupled to ELMy plasma to over 8 MW, considerably enhancing JET research capabilities. This paper provides an overview of the key design features of the ECT system and summarizes the main experimental results achieved so far., Comment: 30 pages, 23 figures

The major aspects linked to the use of the JET auxiliary heating systems: NBI, ICRF and LHCD, in the new JET ITER-like wall (JET-ILW) are presented. We show that although there were issues related to the operation of each system, efficient and safe plasma heating was obtained with room for higher power. For the NBI up to 25.7MW was safely injected; issues that had to be tackled were mainly the beam shine-through and beam re-ionisation before its entrance into the plasma. For the ICRF system, 5MW were coupled in L-mode and 4MW in H-mode; the main areas of concern were RF-sheaths related heat loads and impurities production. For the LH, 2.5 MW were delivered without problems; arcing and generation of fast electron beams in front of the launcher that can lead to high heat loads were the keys issues. For each system, an overview will be given of: the main modifications implemented for safe use, their compatibility with the new metallic wall, the differences in behavior compared with the previous carbon wall, with emphasis on heat loads and impurity content in the plasma., Comment: 21 pages, 17 figures

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 figures

Quantum Monte Carlo estimates of the spectrum of rotationally invariant states of noble gas clusters suggest inter-dimensional degeneracy in $N-1$ and $N+1$ spacial dimensions. We derive this property by mapping the Schr\"odinger eigenvalue problem onto an eigenvalue equation in which $D$ appears as a continuous variable. We discuss implications for quantum Monte Carlo and dimensional scaling methods.

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 figures

A method is introduced to optimize excited state trial wave functions. The method is applied to ground and vibrationally excited states of bosonic van der Waals clusters of upto seven particles. Employing optimized trial wavefunctions with three-body correlations, we use correlation function Monte Carlo to estimate the corresponding excited state energies., Comment: to be published in Recent Advances in Quantum Monte Carlo Methods - Part II, Series: Recent Advances in Computational Chemistry (Vol 2). edited by W. A. Lester, Jr., S. M. Rothstein, and S. Tanaka. World Scientific, Singapore (2001 or 2002)

A quantum Monte Carlo method is introduced to optimize excited state trial wavefunctions. The method is applied in a correlation function Monte Carlo calculation to compute ground and excited state energies of bosonic van der Waals clusters of upto seven particles. The calculations are performed using trial wavefunctions with general three-body correlations.

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.

This paper deals with the optimization of trial states for the computation of dominant eigenvalues of operators and very large matrices. In addition to preliminary results for the energy spectrum of van der Waals clusters, we review results of the application of this method to the computation of relaxation times of independent relaxation modes at the Ising critical point in two dimensions., Comment: 11 pages, 1 figure

In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the underlying mathematics is quite similar in that they are stochastic implementations of the power method. In all cases, optimized trial states can be used to reduce the errors of Monte Carlo estimates.

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.

Compact and accurate wave functions can be constructed by quantum Monte Carlo methods. Typically, these wave functions consist of a sum of a small number of Slater determinants multiplied by a Jastrow factor. In this paper we study the importance of including high-order, nucleus-three-electron correlations in the Jastrow factor. An efficient algorithm based on the theory of invariants is used to compute the high-body correlations. We observe significant improvements in the variational Monte Carlo energy and in the fluctuations of the local energies but not in the fixed-node diffusion Monte Carlo energies. Improvements for the ground states of physical, fermionic atoms are found to be smaller than those for the ground states of fictitious, bosonic atoms, indicating that errors in the nodal surfaces of the fermionic wave functions are a limiting factor., Comment: 9 pages, no figures, Latex

This review covers applications of quantum Monte Carlo methods to quantum mechanical problems in the study of electronic and atomic structure, as well as applications to statistical mechanical problems both of static and dynamic nature. The common thread in all these applications is optimization of many-parameter trial states, which is done by minimization of the variance of the local or, more generally for arbitrary eigenvalue problems, minimization of the variance of the configurational eigenvalue., Comment: 27 pages to appear in " Recent Advances in Quantum Monte Carlo Methods" edited by W.A. Lester

Bosonic van der Waals clusters of sizes three, four and five are studied by diffusion quantum Monte-Carlo techniques. In particular we study the unbinding transition, the ultra-quantum limit where the ground state ceases to exist as a bound state. We discuss the quality of trial wave functions used in the calculations, the critical behavior in the vicinity of the unbinding transition, and simple improvements of the diffusion Monte Carlo algorithm., Comment: World Wide Web URL http://www.phys.uri.edu/people/mark_meierovich/visual/Main.html contains an informal presentation with color graphics

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.

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).

The critical behavior of frustrated Josephson-junction arrays at $f=1/2$ flux quantum per plaquette is considered. Results from Monte Carlo simulations and transfer matrix computations support the identification of the critical behavior of the square and triangular classical arrays and the one-dimensional quantum ladder with the universality class of the XY-Ising model. In the quantum ladder, the transition can happen either as a simultaneous ordering of the $Z_2$ and $U(1)$ order parameters or in two separate stages, depending on the ratio between interchain and intrachain Josephson couplings. For the classical arrays, weak random plaquette disorder acts like a random field and positional disorder as random bonds on the $Z_2$ variables. Increasing positional disorder decouples the $Z_2$ and $U(1)$ variables leading to the same critical behavior as for integer $f$., Comment: 9 pages, Latex, workshop on JJA, to appear in Physica B

In a previous paper (http://www.phys.uri.edu/people/nightingale/publications.html, chem-ph/9406003) we developed a form of variational trial wave function and applied it to van der Waals clusters: five or less atoms of Ar and Ne modeled by the Lennard-Jones potential. In addition, we tested the trial functions for a hypothetical, light atom resembling Ne but with only half its mass. We did not study atoms such as He with larger de Boer parameters, i.e., systems in which the zero point energy plays a more important role relative to the potential energy. This is the main purpose of the present paper. In fact, we study clusters to the very limit where the zero-point energy destroys the ground state as a bound state. A simple picture of this un-binding transition predicts the power law with which the energy vanishes as the de Boer parameter approaches its critical value and the power of the divergence of the the size of the clusters in this limit. Our numerical results are in agreement with these predictions., Comment: text and figures TeX form, 4 pages

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 3.0

Clusters of sizes ranging from two to five are studied by variational quantum Monte Carlo techniques. The clusters consist of Ar, Ne and hypothetical lighter (``$1 \over 2$-Ne") atoms. A general form of trial function is developed for which the variational bias is considerably smaller than the statistical error of currently available diffusion Monte Carlo estimates. The trial functions are designed by a careful analysis of long- and short-range behavior as a function of inter-atomic distance; at intermediate distances, on the order of the average nearest neighbor distance, the trial functions are constructed to have considerable variational freedom. A systematic study of the relative importance of $n$-body contributions to the quality of the optimized trial wave function is made with $2\le n \le 5$. Algebraic invariants are employed to deal efficiently with the many-body interactions., Comment: 19 pages

Thermal and chiral critical exponents of the fully frustrated XY model on a square-lattice are obtained from a finite-size scaling analysis of the free energy of chiral domain walls. Data were obtained by extensive Monte Carlo transfer matrix computations for infinite strips of widths up to $14$ lattice spacings. Two transfer matrices were implemented, one for each of the two principal lattice directions. The results of both are consistent, but the critical exponents differ significantly from the pure Ising values. This is in agreement with other recent Monte Carlo simulations. Our results also support the identification of the critical behavior of this model with that along the line of transitions of simultaneous ordering or becoming critical of Ising and planar rotor degrees of freedom in the XY-Ising model studied recently., Comment: 25 p. w fig. accep. Phys. Rev. B, INPE001