Search results for "Condensed Matter - Statistical Mechanics"
showing 10 items of 508 documents
Logarithmic finite-size effects on interfacial free energies: Phenomenological theory and Monte Carlo studies
2014
The computation of interfacial free energies between coexisting phases (e.g.~saturated vapor and liquid) by computer simulation methods is still a challenging problem due to the difficulty of an atomistic identification of an interface, and due to interfacial fluctuations on all length scales. The approach to estimate the interfacial tension from the free energy excess of a system with interfaces relative to corresponding single-phase systems does not suffer from the first problem but still suffers from the latter. Considering $d$-dimensional systems with interfacial area $L^{d-1}$ and linear dimension $L_z$ in the direction perpendicular to the interface, it is argued that the interfacial …
Shape of crossover between mean-field and asymptotic critical behavior in a three-dimensional Ising lattice
1998
Recent numerical studies of the susceptibility of the three-dimensional Ising model with various interaction ranges have been analyzed with a crossover model based on renormalization-group matching theory. It is shown that the model yields an accurate description of the crossover function for the susceptibility.
Nonlinear response of superparamagnets with finite damping: an analytical approach
2004
The strongly damping-dependent nonlinear dynamical response of classical superparamagnets is investigated by means of an analytical approach. Using rigorous balance equations for the spin occupation numbers a simple approximate expression is derived for the nonlinear susceptibility. The results are in good agreement with those obtained from the exact (continued-fraction) solution of the Fokker-Planck equation. The formula obtained could be of assistance in the modelling of the experimental data and the determination of the damping coefficient in superparamagnets.
Computing absolute free energies of disordered structures by molecular simulation
2009
We present a Monte Carlo simulation technique by which the free energy of disordered systems can be computed directly. It is based on thermodynamic integration. The central idea is to construct an analytically solvable reference system from a configuration which is representative for the state of interest. The method can be applied to lattice models (e.g., the Ising model) as well as off-lattice molecular models. We focus mainly on the more challenging off-lattice case. We propose a Monte Carlo algorithm, by which the thermodynamic integration path can be sampled efficiently. At the examples of the hard sphere liquid and a hard disk solid with a defect, we discuss several properties of the …
Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
1999
Monte Carlo results for the moments of the magnetization distribution of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L (4 \leq L \leq 22) is the linear dimension of a hypercubic lattice with periodic boundary conditions in d=5 dimensions, are analyzed in the critical region and compared to a recent theory of Chen and Dohm (CD) [X.S. Chen and V. Dohm, Int. J. Mod. Phys. C (1998)]. We show that this finite-size scaling theory (formulated in terms of two scaling variables) can account for the longstanding discrepancies between Monte Carlo results and the so-called ``lowest-mode'' theory, which uses a single scaling variable tL^{d/2} where t=T/T_c-1 is the temperature distan…
Effective Cahn-Hilliard Equation for the Phase Separation of Active Brownian Particles
2014
The kinetic separation of repulsive active Brownian particles into a dense and a dilute phase is analyzed using a systematic coarse-graining strategy. We derive an effective Cahn-Hilliard equation on large length and time scales, which implies that the separation process can be mapped onto that of passive particles. A lower density threshold for clustering is found, and using our approach we demonstrate that clustering first proceeds via a hysteretic nucleation scenario and above a higher threshold changes into a spinodal-like instability. Our results are in agreement with particle-resolved computer simulations and can be verified in experiments of artificial or biological microswimmers.
Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling
2018
We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, and the second method is based on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow us to probe a wide range of supersatura…
Test of mode coupling theory for a supercooled liquid of diatomic molecules.I. Translational degrees of freedom
1997
A molecular dynamics simulation is performed for a supercooled liquid of rigid diatomic molecules. The time-dependent self and collective density correlators of the molecular centers of mass are determined and compared with the predictions of the ideal mode coupling theory (MCT) for simple liquids. This is done in real as well as in momentum space. One of the main results is the existence of a unique transition temperature T_c, where the dynamics crosses over from an ergodic to a quasi-nonergodic behavior. The value for T_c agrees with that found earlier for the orientational dynamics within the error bars. In the beta- regime of MCT the factorization of space- and time dependence is satisf…
Density-Functional Theory of Quantum Freezing: Sensitivity to Liquid-State Structure and Statistics
1997
Density-functional theory is applied to compute the ground-state energies of quantum hard-sphere solids. The modified weighted-density approximation is used to map both the Bose and the Fermi solid onto a corresponding uniform Bose liquid, assuming negligible exchange for the Fermi solid. The required liquid-state input data are obtained from a paired phonon analysis and the Feynman approximation, connecting the static structure factor and the linear response function. The Fermi liquid is treated by the Wu-Feenberg cluster expansion, which approximately accounts for the effects of antisymmetry. Liquid-solid transitions for both systems are obtained with no adjustment of input data. Limited …
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum?
2013
An analogy of the Fokker-Planck equation (FPE) with the Schr\"odinger equation allows us to use quantum mechanics technique to find the analytical solution of the FPE in a number of cases. However, previous studies have been limited to the Schr\"odinger potential with a discrete eigenvalue spectrum. Here, we will show how this approach can be also applied to a mixed eigenvalue spectrum with bounded and free states. We solve the FPE with boundaries located at x=\pm L/2 and take the limit L\rightarrow\infty, considering the examples with constant Schr\"{o}dinger potential and with P\"{o}schl-Teller potential. An oversimplified approach was proposed earlier by M.T. Araujo and E. Drigo Filho. A…