Non-Perturbative U(1) Gauge Theory at Finite Temperature

For compact U(1) lattice gauge theory (LGT) we have performed a finite size scaling analysis on $N_{\tau} N_s^3$ lattices for $N_{\tau}$ fixed by extrapolating spatial volumes of size $N_s\le 18$ to $N_s\to\infty$. Within the numerical accuracy of the thus obtained fits we find for $N_{\tau}=4$, 5 and~6 second order critical exponents, which exhibit no obvious $N_{\tau}$ dependence. The exponents are consistent with 3d Gaussian values, but not with either first order transitions or the universality class of the 3d XY model. As the 3d Gaussian fixed point is known to be unstable, the scenario of a yet unidentified non-trivial fixed point close to the 3d Gaussian emerges as one of the possible explanations.Comment: Extended version after referee reports. 6 pages, 6 figure

Stiffening while drying

We present two models for the drying of waterborne paints, which consist of non-volatile latex particles suspended in water. One model considers the water and latex density in a layer as a function of time. Water evaporation at the surface represents the drying. This model results in a one-dimensional free boundary problem, which is solved numerically. Extensions to the model are given that describe the stiffening of the paint. A second model is a particle based dynamical simulation where latex particles form a network through which water particles move. A thin slab of the suspension in a three-dimensional box is studied. Water particles escaping the slab at the surface represent the drying, progressing network formation the stiffening of the paint. Both models allow for validation with material properties as determined experimentally on real coatings

Frequency Dependent Viscosity Near the Critical Point: The Scale to Two Loop Order

The recent accurate measurements of Berg, Moldover and Zimmerli of the viscoelastic effect near the critical point of xenon has shown that the scale factor involved in the frequency scaling is about twice the scale factor obtained theoretically. We show that this discrepancy is a consequence of using first order perturbation theory. Including two loop contribution goes a long way towards removing the discrepancy.Comment: No of pages:7,Submitted to PR-E(Rapid Communication),No of EPS files:

Direct electronic measurement of Peltier cooling and heating in graphene

Thermoelectric effects allow the generation of electrical power from waste heat and the electrical control of cooling and heating. Remarkably, these effects are also highly sensitive to the asymmetry in the density of states around the Fermi energy and can therefore be exploited as probes of distortions in the electronic structure at the nanoscale. Here we consider two-dimensional graphene as an excellent nanoscale carbon material for exploring the interaction between electronic and thermal transport phenomena, by presenting a direct and quantitative measurement of the Peltier component to electronic cooling and heating in graphene. Thanks to an architecture including nanoscale thermometers, we detected Peltier component modulation of up to 15 mK for currents of 20 $\mu$A at room temperature and observed a full reversal between Peltier cooling and heating for electron and hole regimes. This fundamental thermodynamic property is a complementary tool for the study of nanoscale thermoelectric transport in two-dimensional materials.Comment: Final version published in Nature Communications under a Creative Commons Attribution 4.0 International Licens

Glauber dynamics of phase transitions: SU(3) lattice gauge theory

Motivated by questions about the QCD deconfining phase transition, we studied in two previous papers Model A (Glauber) dynamics of 2D and 3D Potts models, focusing on structure factor evolution under heating (heating in the gauge theory notation, i.e., cooling of the spin systems). In the present paper we set for 3D Potts models (Ising and 3-state) the scale of the dynamical effects by comparing to equilibrium results at first and second order phase transition temperatures, obtained by re-weighting from a multicanonical ensemble. Our finding is that the dynamics entirely overwhelms the critical and non-critical equilibrium effects. In the second half of the paper we extend our results by investigating the Glauber dynamics of pure SU(3) lattice gauge on $N_{\tau} N_{\sigma}^3$ lattices directly under heating quenches from the confined into the deconfined regime. The exponential growth factors of the initial response are calculated, which give Debye screening mass estimates. The quench leads to competing vacuum domains of distinct $Z_3$ triality, which delay equilibration of pure gauge theory forever, while their role in full QCD remains a subtle question. As in spin systems we find for pure SU(3) gauge theory a dynamical growth of structure factors, reaching maxima which scale approximately with the volume of the system, before settling down to equilibrium. Their influence on various observables is studied and different lattice sizes are simulated to illustrate an approach to a finite volume continuum limit. Strong correlations are found during the dynamical process, but not in the deconfined phase at equilibrium.Comment: 12 pages, 18 figure

The unreasonable effectiveness of equilibrium-like theory for interpreting non-equilibrium experiments

There has been great interest in applying the results of statistical mechanics to single molecule experiements. Recent work has highlighted so-called non-equilibrium work-energy relations and Fluctuation Theorems which take on an equilibrium-like (time independent) form. Here I give a very simple heuristic example where an equilibrium result (the barometric law for colloidal particles) arises from theory describing the {\em thermodynamically} non-equilibrium phenomenon of a single colloidal particle falling through solution due to gravity. This simple result arises from the fact that the particle, even while falling, is in {\em mechanical} equilibrium (gravitational force equal the viscous drag force) at every instant. The results are generalized by appeal to the central limit theorem. The resulting time independent equations that hold for thermodynamically non-equilibrium (and even non-stationary) processes offer great possibilities for rapid determination of thermodynamic parameters from single molecule experiments.Comment: 6 page

Entropy-based analysis of the number partitioning problem

In this paper we apply the multicanonical method of statistical physics on the number-partitioning problem (NPP). This problem is a basic NP-hard problem from computer science, and can be formulated as a spin-glass problem. We compute the spectral degeneracy, which gives us information about the number of solutions for a given cost $E$ and cardinality $m$. We also study an extension of this problem for $Q$ partitions. We show that a fundamental difference on the spectral degeneracy of the generalized ($Q>2$) NPP exists, which could explain why it is so difficult to find good solutions for this case. The information obtained with the multicanonical method can be very useful on the construction of new algorithms.Comment: 6 pages, 4 figure

Stability diagrams for Landau damping

Coherent modes which are present when there is no incoherent tune spread may be absent when such a spread exists. Such modes are``Landau damped.'' There is instead an incoherent spectrum, a continuum of an infinite number of frequencies, which will decohere (filament), thus not leading to collective instabilities. A stability diagram indicates when Landau damping will be effective. It divides the effective impedance plane, or equivalently the plane of coherent frequency in the absence of tune spread, into regions. The region which contains +i/infinity corresponds to instability. Thus, one can substitute a simpler computation (finding discrete eigenvalues) for a more complex computation (solving an eigenvalue system with both a discrete and a continuous eigenvalue spectrum). We present stability diagrams assuming a linear tune shift with amplitude, allowing tune spread in two transverse planes or in the longitudinal plane alone. When there is longitudinal tune spread, this can not be done exactly, and we describe approximations which make the computation tractable

A comparison of extremal optimization with flat-histogram dynamics for finding spin-glass ground states

We compare the performance of extremal optimization (EO), flat-histogram and equal-hit algorithms for finding spin-glass ground states. The first-passage-times to a ground state are computed. At optimal parameter of tau=1.15, EO outperforms other methods for small system sizes, but equal-hit algorithm is competitive to EO, particularly for large systems. Flat-histogram and equal-hit algorithms offer additional advantage that they can be used for equilibrium thermodynamic calculations. We also propose a method to turn EO into a useful algorithm for equilibrium calculations. Keywords: extremal optimization. flat-histogram algorithm, equal-hit algorithm, spin-glass model, ground state.Comment: 10 LaTeX pages, 2 figure

On the Wang-Landau Method for Off-Lattice Simulations in the "Uniform" Ensemble

We present a rigorous derivation for off-lattice implementations of the so-called "random-walk" algorithm recently introduced by Wang and Landau [PRL 86, 2050 (2001)]. Originally developed for discrete systems, the algorithm samples configurations according to their inverse density of states using Monte-Carlo moves; the estimate for the density of states is refined at each simulation step and is ultimately used to calculate thermodynamic properties. We present an implementation for atomic systems based on a rigorous separation of kinetic and configurational contributions to the density of states. By constructing a "uniform" ensemble for configurational degrees of freedom--in which all potential energies, volumes, and numbers of particles are equally probable--we establish a framework for the correct implementation of simulation acceptance criteria and calculation of thermodynamic averages in the continuum case. To demonstrate the generality of our approach, we perform sample calculations for the Lennard-Jones fluid using two implementation variants and in both cases find good agreement with established literature values for the vapor-liquid coexistence locus.Comment: 21 pages, 4 figure