Monte Carlo renormalization-group calculation for the d=3 Ising model using a modified transformation.

We present a simple approach to high-accuracy calculations of critical properties for the three-dimensional Ising model, without prior knowledge of the critical temperature. The iterative method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group trajectory. We found experimentally that the iterative method enables the calculation of the critical temperature simultaneously with a critical exponent.

Probability, Entropy, and Gibbs' Paradox(es).

Two distinct puzzles, which are both known as Gibbs' paradox, have interested physicists since they were first identified in the 1870s. They each have significance for the foundations of statistical mechanics and have led to lively discussions with a wide variety of suggested resolutions. Most proposed resolutions had involved quantum mechanics, although the original puzzles were entirely classical and were posed before quantum mechanics was invented.

Thermodynamics of finite systems: a key issues review.

A little over ten years ago, Campisi, and Dunkel and Hilbert, published papers claiming that the Gibbs (volume) entropy of a classical system was correct, and that the Boltzmann (surface) entropy was not. They claimed further that the quantum version of the Gibbs entropy was also correct, and that the phenomenon of negative temperatures was thermodynamically inconsistent. Their work began a vigorous debate of exactly how the entropy, both classical and quantum, should be defined.

Surprising convergence of the Monte Carlo renormalization group for the three-dimensional Ising model.

We present a surprisingly simple approach to high-accuracy calculations of the critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different exponents to produce optimal convergence.

Continuity of the entropy of macroscopic quantum systems.

The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper, I analyze and calculate the thermodynamic entropy for large but finite quantum mechanical systems.

Gibbs volume entropy is incorrect.

We show that the expression for the equilibrium thermodynamic entropy contains an integral over a surface in phase space, and in so doing, we confirm that negative temperature is a valid thermodynamic concept. This demonstration disproves the claims of several recent papers that the Gibbs entropy, which contains an integral over a volume in phase space, is the correct definition and that thermodynamics cannot be extended to include negative temperatures. We further show that the Gibbs entropy fails to satisfy the postulates of thermodynamics and that its predictions for systems with nonmonotonic energy densities of states are incorrect.

Efficiency and time-dependent cross correlations in multivariable Monte Carlo updating.

We show that any Monte Carlo (MC) algorithm using joint updates of more than a single variable at each step produces time-shifted correlations between variables-even if the equilibrium probabilities of the variables are independent. These spurious time-shifted correlations will affect both the magnitudes of correlation times and the values of optimal acceptance ratios. In particular, correlation times computed with local variables will not generally give the same predictions of efficiency or optimal acceptance ratios as those computed with global variables.

Monte Carlo renormalization-group analysis of percolation.

We describe a Monte Carlo renormalization group approach to the calculation of critical behavior for percolation models. This approach can be utilized to determine the renormalized bond probabilities and the values of the critical exponents. We illustrate the method for two-dimensional bond percolation, but the method is also applicable to other percolation models and other dimensions.

A model of motor performance during surface penetration: from physics to voluntary control.

The act of puncturing a surface with a hand-held tool is a ubiquitous but complex motor behavior that requires precise force control to avoid potentially severe consequences. We present a detailed model of puncture over a time course of approximately 1,000 ms, which is fit to kinematic data from individual punctures, obtained via a simulation with high-fidelity force feedback. The model describes puncture as proceeding from purely physically determined interactions between the surface and tool, through decline of force due to biomechanical viscosity, to cortically mediated voluntary control.

Comparison of free energy methods for molecular systems.

We present a detailed comparison of computational efficiency and precision for several free energy difference (DeltaF) methods. The analysis includes both equilibrium and nonequilibrium approaches, and distinguishes between unidirectional and bidirectional methodologies. We are primarily interested in comparing two recently proposed approaches, adaptive integration, and single-ensemble path sampling to more established methodologies.

Adaptive integration method for Monte Carlo simulations.

We present an adaptive sampling method for computing free energies, radial distribution functions, and potentials of mean force. The method is characterized by simplicity and accuracy, with the added advantage that the data are obtained in terms of quasicontinuous functions. The method is illustrated and tested with simulations on a high density fluid, including a stringent consistency test involving an unusual thermodynamic cycle that highlights its advantages.

Feeling textures through a probe: effects of probe and surface geometry and exploratory factors.

Vibratory roughness perception occurs when people feel a surface with a rigid probe. Accordingly, perceived roughness should reflect probe and surface geometry, exploratory speed, and force. Experiments 1 and 2 compared magnitude estimation of roughness with the bare finger and two types of probes, one designed to eliminate force moments, under the subject's active control.

Sweeny and Gliozzi dynamics for simulations of Potts models in the Fortuin-Kasteleyn representation.

We compare the correlation times of the Sweeny and Gliozzi dynamics for two-dimensional Ising and three-state Potts models, and the three-dimensional Ising model for the simulations in the percolation representation. The results are also compared with Swendsen-Wang and Wolff cluster dynamics. It is found that Sweeny and Gliozzi dynamics have essentially the same dynamical critical behavior.

Importance of multispin couplings in renormalized Hamiltonians.

We introduce a Monte Carlo approach to the calculation of more distant renormalized interactions with higher accuracy than is possible with previous methods. We have applied our method to study the effects of multispin interactions, which turn out to be far more important than commonly assumed. Even though the individual multispin interactions usually have smaller coupling constants than two-spin interactions, they can dominate the effects of two-spin interactions because they are so numerous.

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.