Monte Carlo modeling of metallic hydrogen: the phase transition and the equation of state

We conducted numerical modeling of atomic (metallic) hydrogen using the PIMC (path integral Monte Carlo) method. The temperature and density range in which the electron (proton) behavior is governed by quantum (classical) statistics was studied. The equations of state in the form of dependences of the internal energy and pressure on temperature and density were obtained in that region. These dependences allow one to reveal and study the phase transition between crystal and liquid phases.     

All-electron path integral Monte Carlo simulations of warm dense matter: application to water and carbon plasmas

We develop an all-electron path integral Monte Carlo method with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. We thereby extend path integral Monte Carlo studies beyond hydrogen and helium to elements with core electrons. Path integral Monte Carlo results for pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics calculations at temperatures of (2.5-7.5)×10(5) K, and both methods together form a coherent equation of state over a density-temperature range of 3-12 g/cm(3) and 10(4)-10(9) K.     

Exchange frequencies in the 2D Wigner crystal

Using path integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a "clean" 2D Wigner crystal as a function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2D (3)He. Using the resulting multispin exchange model we find the spin Hamiltonian for r(s) < or = 175 +/- 10 is a frustrated antiferromagnetic; its likely ground state is a spin liquid. For lower density the ground state will be ferromagnetic.     

Melting of polymer single crystals studied by dynamic Monte Carlo simulations

We report dynamic Monte Carlo simulations of lattice polymers melting from a metastable chain-folded lamellar single crystal. The single crystal was raised and then melted in an ultrathin film of polymers wetting on a solid substrate, mimicking the melting observations made by using Atomic Force Microscopy. We observed that the thickness distribution of the single crystal appears quite inhomogeneous and the thickness increases gradually from facetted edges to the center. Therefore, at low melting temperatures, melting stops at a certain crystal thickness, and melting-recrystallization occurs when allowing crystal thickening; at intermediate temperatures, melting maintains the crystal shape and exhibits different speeds in two stages; at high temperatures, fast melting makes a melting hole in the thinnest region, as well as a saw-tooth-like pattern at the crystal edges. In addition, the linear melting rates at low temperatures align on the curve extrapolated from the linear crystal growth rates. The temperature dependence of the melting rates exhibits a regime transition similar to crystal growth. Such kinetic symmetry persists in the melting rates with variable frictional barriers for c -slip diffusion in the crystal as well as with variable chain lengths. Visual inspections revealed highly frequent reversals upon melting of single chains at the wedge-shaped lateral front of the lamellar crystal. We concluded that the melting kinetics is dominated by the reverse process of intramolecular secondary crystal nucleation of polymers.     

The phases of two-dimensional matter,their transitions,and solid-state stability: A perspective via computer simulation of simple atomic systems

An extensive computer simulation investigation of the structure, thermodynamics and phase stability of the two-dimensional Lennard-Jones system is presented, with special emphasis on the low-pressure melting regime of the phase diagram. This investigation includes isobaric-isothermal Monte Carlo simulations of the various phases of the two-dimensional Lennard-Jones system and of the melting and vaporization processes in configuration space, the isodensity-isothermal Monte Carlo simulations of two-phase coexistence between crystal and liquid and between liquid and vapor, the determination of the phase diagram, the establishment of the thermodynamic melting temperature, and the determination of the physical significance of the Kosterlitz-Thouless-Feynman dislocation model for melting in relation to the stability of the crystalline phase. I conclude that th phase diagram of the Lennard-Jones system in two dimensions is qualitatively similar to that in three dimensions. Finally, I present a new simulation method for doing molecular dynamics at constant pressure and/or constant temperature, and employ this method to study the temporal-spatial evolution of two-dimensional melting and vaporization.     

Off-diagonal long-range order in solid 4He

Measurements of the moment of inertia by Kim and Chan have found that solid (4)He acts like a supersolid at low temperatures. To understand the order in solid 4(He), we have used path integral Monte Carlo simulations to calculate the off-diagonal long-range order (ODLRO) [equivalent to Bose-Einstein condensation (BEC)]. We do not find ODLRO in a defect-free hcp crystal of (4)He at the melting density. We discuss these results in relation to proposed quantum solid trial functions. We conclude that the solid (4)He wave function has correlations which suppress both vacancies and BEC.     

Condensate statistics in one-dimensional interacting Bose gases: exact results

Recently, a quantum Monte Carlo method alternative to the path integral Monte Carlo method was developed for solving the N-boson problem; it is based on the stochastic evolution of classical fields. Here we apply it to obtain exact results for the occupation statistics of the condensate mode in a weakly interacting trapped one-dimensional Bose gas. The temperature is varied across the critical region down to temperatures lower than the trap level spacing. We also derive the condensate statistics in the Bogoliubov theory: this reproduces the exact results at low temperature and explains the suppression of odd numbers of noncondensed particles at T approximately 0.     

固体氢的压缩行为

 同时考虑分子的平动与转动自由度，用等温等压系综的路径积分蒙特卡罗方法研究了固体氢的状态方程。在有实验数据的区域，计算结果同实验结果符合很好，在无实验数据的超高压区域，计算结果同实验的外推结果符合。为了定量研究零点运动，还计算了体系的能量。     

Counterions at highly charged interfaces: from one plate to like-charge attraction

We present an analytical approach for similarly and highly charged planar interfaces in the presence of counterions. The procedure is physically transparent and based on an exact low temperature expansion around the ground state formed by the two-dimensional Wigner crystal of counterions. The one plate problem is worked out, together with the two plates situation. Unlike previous approaches, the expansion is free of divergences, and is shown to be in excellent agreement with available data of Monte?Carlo simulations under strong Coulombic couplings. In the two plates case, the present results shed light on the like-charge attraction regime.     

Dielectric properties and compensation behaviors of a monolayer naphthalene-like nanoisland: Monte Carlo simulations

In this paper, we propose a model to study the thermal and dielectric properties of a monolayer naphthalene-like nanoisland. The ferrielectric mixed spin (1, 7/2) Blume-Capel Ising model has been studied, using Monte Carlo simulations under the Metropolis algorithm. The ground state phase diagrams, in the absence of temperature, are investigated. Moreover, we illustrated the thermal and dielectric properties as a function of temperature, for fixed values of the other parameters. On the other hand, we examine the effects of the exchange coupling interactions on the compensation and blocking temperatures. In addition, we explore the effects of crystal and external longitudinal electric fields on total polarizations.     

磁通格子的有序-无序相变和反向熔化

考虑了无序钉扎、热涨落和磁通互作用, 用Monte Carlo分子动力学模拟方法研究二维磁通格子在无序钉扎强度和温度空间的相图, 以及由布拉格玻璃相到非晶磁通玻璃相和到磁通液体相的有序-无序相变.为了决定磁通格子的序，计算了静态结构因子和磁通格子位形的有限尺寸指数.计算结果表明，Bragg玻璃相在低温的无序磁通玻璃相和高温的磁通液体相之间 , 表现出磁通格子的反向熔化行为.分析后认为，这一反向熔化行为起因于磁通之间互作用的温度效应. 关键词： Ⅱ类超导体 磁通格子 相图 结构因子 反向熔化     

Melting of bosonic stripes

We use quantum Monte Carlo simulations to determine the finite temperature phase diagram and to investigate the thermal and quantum melting of stripe phases in a two-dimensional hard-core boson model. At half filling and low temperatures the stripes melt at a first order transition. In the doped system, the melting transitions of the smectic phase at high temperatures and the superfluid smectic (supersolid) phase at low temperatures are either very weakly first order, or of second order with no clear indications for an intermediate nematic phase.     

Phase diagram in the quantum XY model with long-range interactions

We study the d-dimensional quantum XY model with ferromagnetic long-range interaction decaying as r-p in terms of boson operators, by employing the coherent state path integral approach. We have obtained a finite critical temperature as a function of the dimension (d) for d2d the system becomes disordered at all temperatures. For the particular values p=3/2 and d=1 our theoretical calculations are comparable to those from Monte Carlo simulations.     

Single molecule acid-base kinetics and thermodynamics

We report a method in which temperature dependent single-molecule fluorescence measurements are used to study the kinetics and thermodynamics of the acid-base interaction in films of photoresist polymer. We use the two distinct fluorescent prototropic forms of Coumarin 6 (C6-->C6+) to indicate the state of the acid-base system. Data are analyzed using a statistical model of the intensity probability distributions, yielding temperature dependent proton exchange rates, which is confirmed through agreement with a simple two-state Monte Carlo model. The temperature dependent rates are used to calculate the activation enthalpy for proton exchange.     

Modelling Quasicrystals at Positive Temperature

We consider a two-dimensional lattice model of equilibrium statistical mechanics, using nearest neighbor interactions based on the matching conditions for an aperiodic set of 16 Wang tiles. This model has uncountably many ground state configurations, all of which are nonperiodic. The question addressed in this paper is whether nonperiodicity persists at low but positive temperature. We present arguments, mostly numerical, that this is indeed the case. In particular, we define an appropriate order parameter, prove that it is identically zero at high temperatures, and show by Monte Carlo simulation that it is nonzero at low temperatures.     

Finite Size Effect in Path Integral Monte Carlo Simulations of 4He Systems

Path integral Monte Carlo (PIMC) simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of ⁴He. We determine the energy as a function of temperature at saturated-vapor-pressure (SVP) conditions in the temperature range of T∈[1.0 K, 4.0 K], and the equation of state (EOS) in the ground state for systems consisted of 32, 64 and 128 ⁴He atoms, respectively. We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T∈[2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.     

Ordering and domains in tetragonal crystals of Ising spins coupled via dipolar interactions

Dipolar coupling in the body-centered tetragonal crystal of Ising spins that is a prototype of the Mn₁₂Ac molecular magnet favors ferromagnetic ordering below the mean-field Curie temperature 0.71 K. With the help of Monte Carlo on crystals of up to one million Mn₁₂ molecules, it is shown that ordering occurs at 0.36 K in elongated crystals. The resulting state is split into ferromagnetic domains with domain walls preferring the diagonal orientation. Domain walls are pinned by the lattice at low temperatures. Making the crystal shorter makes domains finer and smoothens out the singularity at the ordering transition, decreasing the susceptibility in the domain state.     

铁磁键稀疏Blume-Capel模型相图的Monte Carlo研究

本文应用Monte Carlo方法求得铁磁键稀疏平方点阵的Blume-Capel模型的相图。利用有限尺寸的标度理论,得到晶场为零时的相变温度,并同其他方法所得的结果作了比较。同时用Monte Carlo方法确定了键稀疏时三临界点的值对键浓度的依赖关系。 关键词：     

Dislocation lines as the precursor of the melting of crystalline solids observed in Monte Carlo simulations

The microscopic mechanism of the melting of a crystal is analyzed by the constant-pressure Monte Carlo simulation of a Lennard-Jones fcc system. Beyond a temperature of the order of 0.8 of the melting temperature, we found that the relevant excitations are lines of defects. Each of these lines has the structure of a random walk of various lengths on an fcc defect lattice. We identify these lines with the dislocation ones proposed in recent phenomenological theories of melting. Near melting we find the appearance of long lines that cross the whole system. We suggest that these long lines are the precursor of the melting process.     

Molecular dynamics study for the melting curve of MgO at high pressure

Shell-model molecular dynamics method is used to study the melting temperatures of MgO at elevated temperatures and high pressures using interaction potentials. Equations of state for MgO simulated by molecular dynamics are in good agreement with available experimental data. The pressure dependence of the melting curve of MgO has been calculated. The surface melting and superheating are considered in the correction of experimental data and the calculated values, respectively. The results of corrections are compared with those of previous work. The corrected melting temperature of MgO is consistent with corrected experimental measurements. The melting temperature of MgO up to 140GPa is calculated.