Inverse Monte Carlo renormalization group transformations for critical phenomena

We introduce a computationally stable inverse Monte Carlo renormalization group transformation method that provides a number of advantages for the calculation of critical properties. We are able to simulate the fixed point of a renormalization group for arbitrarily large lattices without critical slowing down. The log-log scaling plots obtained with this method show remarkable linearity, leading to accurate estimates for critical exponents. We illustrate this method with calculations in two- and three-dimensional Ising models for a variety of renormalization group transformations.     

Hyperfine experiments on magnetic critical phenomena

The application of hyperfine techniques to the study of magnetic critical phenomena is selectively reviewed. Topics discussed are probe independence, the test of universality via measurements of static exponents, static exponents in disordered systems, and dynamic critical phenomena.Work supported in part by the National Science Foundation.     

Monte Carlo analysis of experiments on individual adatoms

Quantitative studies of individual adatom motion using the field ion microscope are difficult in as much as the number of observations is limited. However, simulations by Monte Carlo techniques make it possible to maximize the information obtained from small statistical samples. Questions encountered in studying the diffusion and interaction of adatoms have therefore been examined by simulation, and results are presented for the following topics: (1) Corrections for the finite size of planes on which atomic diffusion is observed. (2) Statistical scatter in the estimation of diffusion parameters from the temperature dependence of the mean-square displacement. (3) Conditions for measuring rates of single- and double-length jumps in atomic diffusion. (4) Uncertainties in the estimation of interaction energies from pair distribution measurements.     

The time scale of Monte Carlo experiments

The time required to reach equilibrium in a standard Monte Carlo experiment is estimated on the basis of exact bounds on the longest time scale in one-dimensional models. The result implies the empirical law of Arrhenius at low temperatures if there are energy barriers.     

Variational Monte Carlo study of pentaquark states

Accurate numerical solution of the five-body Schr?dinger equation is effected via variational Monte Carlo calculations. The spectrum is assumed to exhibit a narrow resonance with strangeness S = +1. A fully antisymmetrized and pair-correlated five-quark wave function is obtained for the assumed nonrelativistic Hamiltonian, which has spin, isospin, and color dependent pair interactions and many-body confining terms, which are fixed by the nonexotic spectra. Gauge field dynamics are modeled via flux-tube exchange factors. The energy determined for the ground states with J(pi) = (1/2)- ((1/2)+) is 2.22 (2.50) GeV. A lower energy negative parity state is consistent with recent lattice results. The short-range structure of the state is analyzed via its diquark content.     

Quantum Monte Carlo studies of bound and unbound states

Over the last fifteen years, there has been tremendous progress in understanding how nuclear structure arises from the nucleon-nucleon interaction. I describe the contribution to this progress made by quantum Monte Carlo computational methods, as well as directions to be taken in future work. Most effort in the past has concentrated on energy spectra, and we have had good success in computing the spectra of systems with A≤12. We are now shifting our attention to off-diagonal and scattering/reaction properties of the light nuclei. I also discuss briefly the relation of quantum Monte Carlo methods to other ab initio methods and their particular relevance for weakly-bound nuclei produced at radioactive-beam facilities.     

Variational quantum Monte Carlo simulations with tensor-network states

We show that the formalism of tensor-network states, such as the matrix-product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of this approach by explicit MPS calculations for the transverse Ising chain with up to N=256 spins at criticality, using periodic boundary conditions and D x D matrices with D up to 48. The computational cost of our scheme formally scales as ND3, whereas standard MPS approaches and the related density matrix renormalization group method scale as ND5 and ND6, respectively, for periodic systems.     

Transient non-linear phenomena and metastable states of charge-density waves in niobium triselenide

Details are given of the transient response of NbSe₃ at 42 K to currents I(t) of various repetitive pulsed waveforms. Nonlinear conduction, due supposedly to motion of one of the two charge-density waves (CDWs) present, was measured as U(t) = IR₀ ? V, where V(t) is the voltage developed across the specimen and R₀ is its resistance in the Ohmic regime.With unidirectional pulses two threshold currents for nonlinearity were observed. On passing the lower threshold, a gradual rise (time-constant 50 μs) of U towards the d.c. value was seen; this behaviour was shown not to originate in the inertia of the CDW, and probably arose thermally. Only after the second threshold was passed did U appear to rise immediately current was applied. The existence of two thresholds accounts for a discrepancy between pulsed and d.c. measurements of conductivity noted by Brill et al. (1981), and also for a phenomenon previously attributed to “locking” between the two CDWs [6].When the pulses were alternately negative- and positive-going, |U| rose beyond its eventual (d.c.) value, towards which it subsequently decayed. A study of this “overshoot” phenomenon has shown the speciment to be left, after a current pulse, in a long-lived metastable state in which pinning stabilises some distortion of the CDW, presumably similar to that of which recent electron micrographs [11] appear to be evidence.A simple model, associating the overshoot with transitions between metastable states, adequately describes the conditions for its occurrence. However, the origin of the conduction associated with the moving CDW remains uncertain, both the Frohlich mechanism and a single-electron alternative finding some experimental support.     

Non-equilibrium critical phenomena and phase transitions into absorbing states

This review addresses recent developments in non-equilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic non-equilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.     

Monte Carlo study of the effect of perturbations on critical droplets

We present a Monte Carlo study of the effect of perturbations on critical or nucleation droplets in both classical and spinodal nucleation. Locating the saddle point with an intervention technique, we determine that the effect of perturbations at the saddle point depends on their location in the droplet. We find that the most effective perturbations occur at the location of the maximum growth rate where the droplet is allowed to nucleate and grow unperturbed. Moreover, the decay of sufficiently perturbed droplets follows a path that can be best characterized as a growth mode in reverse, specifically the decay of classical droplets is at the surface and that of spinodal droplets at the center independent of the location of the perturbation.     

Monte Carlo event generators for NICA/MPD and CBM experiments

An improved version of the Glauber Monte Carlo simulation program is proposed that allows on to estimate the geometric properties of nucleus–nucleus interactions in energy range \(\sqrt {{S_{NN}}} \) of 5 GeV to 20 TeV. It is shown that the geometric properties of interactions at energies of 5–10 GeV (NICA/MPD and CBM) are quite close to those at an energy of 200 GeV (RHIC). The geometric properties can be derived from experimentally observable quantities using different techniques. The most promising of these is the registration of spectator neutrons from nuclear residuals. It is shown that event generators predict different multiplicities of produced neutrons. The registration of neutrons will be a great step in our understanding of the decay of nuclei in highly excited states.     

Glauber Monte Carlo program for NICA/MPD and CBM experiments

A program code widely applied at RHIC and LHC for calculations of geometrical properties of nucleus-nucleus interactions is adapted for NICA/MPD and CBM energies. A parameterization of pp elastic scattering amplitude earlier proposed by the authors and valid at √s ≥ 3 GeV is used for a setting of the nucleon-nucleon collision profile. An approach well known in physics of low and intermediate energies is used for a determination of nuclear parameters. The code is enlarged by a possibility to account for the Gribov inelastic screening.     

Monte Carlo studies of percolation phenomena for a simple cubic lattice

The site-percolation problem on a simple cubic lattice is studied by the Monte Carlo method. By combining results for periodic lattices of different sizes through the use of finite-size scaling theory we obtain good estimates forp _c (0.3115±0.0005), (0.41±0.01), (1.6±0.1), and(0.8±0.1). These results are consistent with other studies. The shape of the clusters is also studied. The average surface area for clusters of sizek is found to be close to its maximal value for the low-concentration region as well as for the critical region. The percentage of particles in clusters of different sizesk is found to have an exponential tail for large values ofk forP <p _c. Forp >p _c there is too much scatter in the data to draw firm conclusions about the size distribution.Work supported in part by USAFOSR Grant #73-2430B and by ERDA #E(11-1)-3077.