Previously, we have presented a methodology to extend canonical Monte Carlo methods inspired on a suitable extension of the canonical fluctuation relation $C=β^{2}<δE^{2}>$ compatible with negative heat capacities $C<0$. Now, we improve this methodology by introducing a better treatment of finite size effects affecting the precision of a direct determination of the microcanonical caloric curve $β(E) =\partial S(E) /\partial E$, as well as a better implementation of MC schemes. We shall show that despite the modifications considered, the extended canonical MC methods possibility an impressive overcome of the so-called \textit{super-critical slowing down} observed close to the region of a temperature driven first-order phase transition. In this case, the dependence of the decorrelation time $τ$ with the system size $N$ is reduced from an exponential growth to a weak power-law behavior $τ(N)\propto N^α$, which is shown in the particular case of the 2D seven-state Potts model where the exponent $α=0.14-0.18$.
We present a practical analysis of the fermion sign problem in fermionic path integral Monte Carlo (PIMC) simulations in the grand-canonical ensemble (GCE). As a representative model system, we consider electrons in a $2D$ harmonic trap. We find that the sign problem in the GCE is even more severe than in the canonical ensemble at the same conditions, which, in general, makes the latter the preferred option. Despite these difficulties, we show that fermionic PIMC simulations in the GCE are still feasible in many cases, which potentially gives access to important quantities like the compressibl…
We present a method to facilitate Monte Carlo simulations in the grand canonical ensemble given a target mean particle number. The method imposes a fictitious dynamics on the chemical potential, to be run concurrently with the Monte Carlo sampling of the physical system. Corrections to the chemical potential are made according to time-averaged estimates of the mean and variance of the particle number, with the latter being proportional to thermodynamic compressibility. We perform a variety of tests, and in all cases find rapid convergence of the chemical potential -- inexactness of the tuning …
Monte-Carlo sampling of lattice model Hamiltonians is a well-established technique in statistical mechanics for studying the configurational entropy of crystalline materials. When species to be distributed on the lattice model carry charge, the charge balance constraint on the overall system prohibits single-site Metropolis exchanges in MC. In this article, we propose two methods to perform MC sampling in the grand-canonical ensemble in the presence of a charge-balance constraint. The table-exchange method (TE) constructs small charge-conserving excitations, and the square-charge bias method (…
A classical density functional theory (cDFT) based on the PC-SAFT equation of state is proposed for the calculation of adsorption equilibria of pure substances and their mixtures in covalent organic frameworks (COFs). Adsorption isotherms of methane, ethane, n-butane and nitrogen in the COFs TpPa-1 and 2,3-DhaTph are calculated and compared to results from grand canonical Monte Carlo (GCMC) simulations. Mixture adsorption is investigated for the methane/ethane and methane/n-butane binary systems. Excellent agreement between PC-SAFT DFT and GCMC is obtained for all adsorption isotherms up to pr…
A systematic Monte Carlo simulation study of the primitive model electrical double layer over an extended range of concentrations, electrode charges, cation diameters and valences
本研究的目的是提供数据的原始模型的双电层，其中离子被建模为带电的硬球，溶剂作为一个隐含的介电背景（与介电常数$ε= 78.5$），和电极作为一个光滑的，均匀带电的，硬壁。我们使用正则和巨正则蒙特卡罗模拟来计算浓度分布，并通过求解泊松方程来获得电场和静电势分布。我们报告了一个扩展范围的参数，包括1：1，2：1和3：1的电解质浓度$c=0.0001-1$ M附近的电极携带表面电荷高达$σ=\pm 0.5$ Cm $^{-2}$。阴离子是一价的，具有固定的直径$d_{-}=3$ Ω，而阳离子的电荷和直径在$z_{+}=1$，2、3和$d_{+}=1.5$，3、6和9 Ω的范围内变化（温度为$298.15$ K）。我们在支持性信息中提供了所有原始数据。
