Lattice Monte Carlo Simulations Research Articles

Surface-Initiated Polymerization with an Initiator Gradient: A Monte Carlo Simulation.

Due to the difficulty of accurately characterizing properties such as the molecular weight (Mn) and grafting density (σ) of gradient brushes (GBs), these properties are traditionally assumed to be uniform in space to simplify analysis. Applying a stochastic reaction model (SRM) developed for heterogeneous polymerizations, we explored surface-initiated polymerizations (SIPs) with initiator gradients in lattice Monte Carlo simulations to examine this assumption. An initial exploration of SIPs with 'homogeneously' distributed initiators revealed that increasing σ slows down the polymerization process, resulting in polymers with lower molecular weight and larger dispersity (Đ) for a given reaction time. In SIPs with an initiator gradient, we observed that the properties of the polymers are position-dependent, with lower Mn and larger Đ in regions of higher σ, indicating the non-uniform properties of polymers in GBs. The results reveal a significant deviation in the scaling behavior of brush height with σ compared to experimental data and theoretical predictions, and this deviation is attributed to the non-uniform Mn and Đ.

Mitigating topological freezing using out-of-equilibrium simulations

Motivated by the recently-established connection between Jarzynski’s equality and the theoretical framework of Stochastic Normalizing Flows, we investigate a protocol relying on out-of-equilibrium lattice Monte Carlo simulations to mitigate the infamous computational problem of topological freezing. We test our proposal on 2d CPN−1 models and compare our results with those obtained adopting the Parallel Tempering on Boundary Conditions proposed by M. Hasenbusch, obtaining comparable performances. Our work thus sets the stage for future applications combining our Monte Carlo setup with machine learning techniques.

Hydrogen on screw dislocation in Fe and W: Existence of 3D-compound and exotic segregation profile

We present the study of hydrogen atom segregation on screw dislocation in Fe and W metals by means of rigid lattice Monte Carlo simulations using interaction energies obtained from ab initio calculations. These interaction energies are attractive or repulsive depending on direction and distance. This high interaction anisotropy leads to the formation of a 3D compound for both iron and tungsten. A second consequence is that, within a given temperature range, hydrogen enrichment is greater at the outer than at the innermost sites of the dislocation. This unusual behavior is only observed for iron. We propose a mean-field model that accounts for the ordering phenomenon to explain the results and the differences between the two metals.

The topological susceptibility slope χ′ of the pure-gauge SU(3) Yang-Mills theory

We determine the pure-gauge SU(3) topological susceptibility slope χ′, related to the next-to-leading-order term of the momentum expansion of the topological charge density 2-point correlator, from numerical lattice Monte Carlo simulations. Our strategy consists in performing a double-limit extrapolation: first we take the continuum limit at fixed smoothing radius, then we take the zero-smoothing-radius limit. Our final result is χ′ = [17.1(2.1) MeV]2. We also discuss a theoretical argument to predict its value in the large-N limit, which turns out to be remarkably close to the obtained N = 3 lattice result.

Reduction of Magnetic Interaction Due to Clustering in Doped Transition-Metal Dichalcogenides: A Case Study of Mn-, V-, and Fe-Doped WSe2.

Using Hubbard-U-corrected density functional theory calculations, lattice Monte Carlo simulations, and spin Monte Carlo simulations, we investigate the impact of dopant clustering on the magnetic properties of WSe2 doped with period four transition metals. We use manganese (Mn) and iron (Fe) as candidate n-type dopants and vanadium (V) as the candidate p-type dopant, substituting the tungsten (W) atom in WSe2. Specifically, we determine the strength of the exchange interaction in Fe-, Mn-, and V-doped WSe2 in the presence of clustering. We show that the clusters of dopants are energetically more stable than discretely doped systems. Further, we show that in the presence of dopant clustering, the magnetic exchange interaction significantly reduces because the magnetic order in clustered WSe2 becomes more itinerant. Finally, we show that the clustering of the dopant atoms has a detrimental effect on the magnetic interaction, and to obtain an optimal Curie temperature, it is important to control the distribution of the dopant atoms.

Higher orders for cosmological phase transitions: a global study in a Yukawa model

We perform a state-of-the-art global study of the cosmological thermal histories of a simple Yukawa model, and find higher perturbative orders to be important for determining both the presence and strength of strong first-order phase transitions. Using high-temperature effective field theory, we calculate the free energy density of the model up to O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(y5T4), where y is the Yukawa coupling and T is the temperature. The locations of phase transitions are found using the results of lattice Monte-Carlo simulations, and the strength of first-order transitions are evaluated within perturbation theory, to 3-loop order. This is the first global study of any model at this order. Compared to a vanilla 1-loop analysis, accurate to O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(y2T4), reaching such accuracy enables on average a five-fold reduction in the relative uncertainty in the predicted critical temperature Tc, and an additional ∼ 50% strong first-order transitions with latent heat L/Tc4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ L/{T}_c^4 $$\\end{document}> 0.1 to be identified in our scan.

Atomistic models of In and Ga diffusion in Cu(In,Ga)Se2

To improve the performance of Cu(In,Ga)Se2 thin-film photovoltaic devices, a robust understanding of the dominant diffusion pathways of the alloy species In and Ga is needed. Here, the most probable defect complexes and mechanisms for In and Ga diffusion are identified with the aid of density functional theory. The binding energies and migration barriers for these complexes are calculated in bulk CuInSe2 and CuGaSe2. Analytic models and kinetic lattice Monte Carlo simulations are employed to predict the diffusivity of In and Ga under variations in composition and temperature. We find that a model based on coulombic interactions between group III antisites and vacancies on the Cu-sublattice produces results that match well with experiment.

Multistep molecular mechanisms of Aβ16-22 fibril formation revealed by lattice Monte Carlo simulations.

As a model of self-assembly from disordered monomers to fibrils, the amyloid-β fragment Aβ16-22 was subject to past numerous experimental and computational studies. Because dynamics information between milliseconds and seconds cannot be assessed by both studies, we lack a full understanding of its oligomerization. Lattice simulations are particularly well suited to capture pathways to fibrils. In this study, we explored the aggregation of 10 Aβ16-22 peptides using 65 lattice Monte Carlo simulations, each simulation consisting of 3 × 109 steps. Based on a total of 24 and 41 simulations that converge and do not converge to the fibril state, respectively, we are able to reveal the diversity of the pathways leading to fibril structure and the conformational traps slowing down the fibril formation.

An Efficient Method to Generate Dense Amorphous Structures for Molecular Simulation of Vinyl Polymers

AbstractAn efficient technique to construct dense amorphous polymers at the bulk density is illustrated for two vinyl polymers, i.e., PVX, –[CH2–CH(X)]–. Bulk amorphous polypropylene (PP) and polystyrene (PS) structures are generated starting from coarse‐graining polymer chains and are mapped onto the second nearest neighbor diamond (2nnd) lattice. PVX are represented by the rotational isomeric state (RIS) model and non‐bonded interactions are treated by the Lennard–Jones (LJ) potential function. Lattice Monte Carlo (MC) simulation is utilized to equilibrate coarse‐grained (C) PVX and the fully atomistic models can be recovered by the reverse‐mapping procedure to restore the missing atoms. After geometry optimization, chain and material properties of bulk PVX structure are computed to validate the atomistic models including conformational characteristics, Hildebrand solubility parameter, pair correlation function, and scattering structure factor.

Lattice determination of the topological susceptibility slope χ′ of 2d CPN−1 models at large N

We compute the topological susceptibility slope $\chi^\prime$, related to the second moment of the two-point correlator of the topological charge density, of $2d$ $\mathrm{CP}^{N-1}$ models for $N=5,11,21$ and $31$ from lattice Monte Carlo simulations. Our strategy consists in performing a double limit: first, we take the continuum limit of $\chi^\prime$ at fixed smoothing radius in physical units; then, we take the zero-smoothing-radius limit. Since the same strategy can also be applied to $4d$ gauge theories and full QCD, where $\chi^\prime$ plays an intriguing theoretical and phenomenological role, this work constitutes a step towards the lattice investigation of this quantity in such models.

Influence of ordering phenomena on carbon segregation in tungsten screw dislocation

Concentration profiles on the different sites of tungsten screw dislocation are calculated as a function of the nominal carbon atom concentration, temperature and dislocation density. Rigid lattice Monte Carlo simulations and associated mean-field modelling are performed based on interaction energies from ab initio calculations. We show that the repulsive interactions induce ordering phenomena that drastically change the concentration in the core of the dislocation and leads to ordered structures among the octahedral sites. We detail the domains of short-range ordering (SRO) and long-range ordering (LRO).

The influence of cross-interactions between dilute cosolutes upon liquid interfaces.

We employ a statistical mechanical dilute solution theory (DST) and lattice Monte Carlo simulations to investigate the interfacial properties of ternary solutions with a dominant solvent and two dilute cosolutes. We consider cosolutes with weak interfacial preferences in order to focus on the impact of cross-interactions between the two cosolute species. When the cross-interaction is properly balanced, the two cosolutes make independent, additive contributions to both bulk and interfacial properties. Conversely, repulsive cross-interactions slightly enhance the interfacial preference of both solutes. In contrast, attractive cross-interactions reduce interfacial preferences and can convert weak surfactants into weak depletants. We observe a particularly interesting transition in the symmetric case of two equivalent self-repelling cosolutes with attractive cross-interactions. In this regime, the major cosolute acts as a weak surfactant in order to avoid repulsive self-interactions, while the minor cosolute acts as a weak depletant in order to form attractive cross-interactions. The two equivalent cosolutes switch roles depending upon their relative concentration. DST very accurately describes the surface tension and surface excess of simulated lattice solutions up to molar concentrations. More importantly, DST provides quantitative and qualitative insight into the mechanism by which cosolute interactions modulate interfacial preferences.

Velocity of sound beyond the high-density relativistic limit from lattice simulation of dense two-color QCD

Abstract We obtain the equation of state (EoS) for two-color quantum chromodynamics (QCD) at low temperature and high density from the lattice Monte Carlo simulation. We find that the velocity of sound exceeds the relativistic limit ($c_s^2/c^2=1/3$) after BEC-BCS (Bose-Einstein condensation–Bardeen–Cooper–Schrieffer) crossover in the superfluid phase. Such an excess of the sound velocity is previously unknown from any lattice calculations for QCD-like theories. This finding might have a possible relevance to the EoS of neutron star matter revealed by recent measurements of neutron star masses and radii.

Nonperturbative Decoupling of Massive Fermions.

SU(2) gauge theory with N_{f}=24 massless fermions is noninteracting at long distances, i.e., it has an infrared fixed point at vanishing coupling. With massive fermions, the fermions are expected to decouple at energy scales below the fermion mass, and the infrared behavior is that of confining SU(2) pure gauge theory. We demonstrate this behavior nonperturbatively with lattice MonteCarlo simulations by measuring the gradient flow running coupling.

Lattice Monte Carlo simulations with two impurity worldlines

We develop the impurity lattice Monte Carlo formalism for the case of two distinguishable impurities in a bath of polarized fermions. The majority particles are treated as explicit degrees of freedom, while the impurities are described by worldlines. The latter serve as localized auxiliary fields, which affect the majority particles. We apply the method to non-relativistic three-dimensional systems of two impurities and a number of majority particles where both the impurity–impurity interaction and the impurity–majority interaction have zero range. We consider the case of an attractive impurity–majority interaction, and we study the formation and disintegration of bound states as a function of the impurity–impurity interaction strength. We also discuss the potential applications of this formalism to other quantum many-body systems.

Identifying magnetic antiskyrmions while they form with convolutional neural networks

Chiral magnets have attracted a large amount of research interest in recent years because they support a variety of topological defects, such as skyrmions and bimerons, and allow for their observation and manipulation through several techniques. They also have a wide range of applications in the field of spintronics, particularly in developing new technologies for memory storage devices. However, the vast amount of data generated in these experimental and theoretical studies requires adequate tools, among which machine learning is crucial. We use a Convolutional Neural Network (CNN) to identify the relevant features in the thermodynamical phases of chiral magnets, including (anti-)skyrmions, bimerons, and helical and ferromagnetic states. We use a flexible multi-label classification framework that can correctly classify states in which different features and phases are mixed. We then train the CNN to predict the features of the final state from snapshots of intermediate states of a lattice Monte Carlo simulation. The trained model allows identifying the different phases reliably and early in the formation process. Thus, the CNN can significantly speed up the large-scale simulations for 3D materials that have been the bottleneck for quantitative studies so far. Moreover, this approach can be applied to the identification of mixed states and emerging features in real-world images of chiral magnets.

Nonperturbative test of the Maldacena-Milekhin conjecture for the BMN matrix model

We test a conjecture by Maldacena and Milekhin for the ungauged version of the Berenstein-Maldacena-Nastase (BMN) matrix model by lattice Monte Carlo simulation. The numerical results reproduce the perturbative and gravity results in the limit of large and small flux parameter, respectively, and are consistent with the conjecture.

Diffusivity interfaces in lattice Monte Carlo simulations: Modeling inhomogeneous delivery and release systems.

Lattice Monte Carlo (LMC) simulations are widely used to investigate diffusion-controlled problems such as drug-release systems. The presence of an inhomogeneous diffusivity environment raises subtle questions about the interpretation of stochastic dynamics in the overdamped limit, an issue sometimes referred to as the "Ito-Stratonovich-isothermal dilemma." We propose a LMC formalism that includes the different stochastic interpretations in order to model the diffusion of particles in a space-dependent diffusivity landscape. Using as an example a simple inhomogeneous one-dimensional system with a diffusivity interface and different boundary conditions, we demonstrate that we can properly reproduce the steady state and dynamic properties of these systems and that these properties do depend on the choice of calculus. In particular, we argue that the version of the LMC algorithm that uses Ito calculus, which is commonly used to model drug delivery systems, should be replaced by the isothermal version for most applications. Our LMC methodology provides an efficient alternative to Langevin simulations for a wide class of space-dependent diffusion problems.

Conformation and structure of ring polymers in semidilute solutions: A molecular dynamics simulation study

Scaling is one of the most fundamental concepts in theoretical polymer physics. For linear polymers in semidilute solutions under a good solvent condition, there has been a well established scaling behavior of mean-square radius of gyration of chains with the concentration, i.e., R g 2 ~ ϕ β , with β = −0.25, which receives strong support from experiments, computer simulations and scaling arguments. However, a clear-cut conclusion about the scaling behavior of dimensions of nonconcatenated and unknotted ring polymers in the semidilute solution with the concentration has not been achieved. Values of the corresponding scaling exponent β are diversely reported in literature, ranging from −0.25 to −0.59 and in contradiction within experimental, simulation and theoretical studies. As an endeavour for clarifying this issue, we carried out extensive molecular dynamics (MD) simulations based on the Kremer-Grest model of ring polymers with chain lengths N up to 5120 in semidilute solutions, and compared our results about ring conformations with almost all of experimental, simulation and theoretical data available in literature. Our MD simulation results lead to a conclusion that the mean-square radius of gyration of ring polymers scales with the concentration in semidilute regime as R g 2 ∼ φ − 0.59 ± 0.01 . This conclusion is in a good agreement with a previous finding by a lattice Monte Carlo simulation. Surprisingly, by looking into the experimental and other simulation results reported previously with sufficient caution, we tend to conclude that in reality almost all of their data can be described reasonably well by the same scaling law, R g 2 ~ ϕ − 0.59 . Furthermore, the scaling exponent obtained (−0.59) can be successfully explained by a scaling argument based on concept of correlation length. Finally, effects of the concentration on shape properties and packing behavior of ring polymers in the semidilute solutions have also been illuminated within our MD simulations. • Scaling behavior of ring dimensions in semidilute solutions with the concentration has been revisited. • Comparison of our results with experimental, and other simulation and theoretical results has been conducted. • Effect of concentration on shape and packing behavior of ring polymers in semidilute solutions has been illuminated.

Confinement/deconfinement transition in the D0-brane matrix model — A signature of M-theory?

We study the confinement/deconfinement transition in the D0-brane matrix model (often called the BFSS matrix model) and its one-parameter deformation (the BMN matrix model) numerically by lattice Monte Carlo simulations. Our results confirm general expectations from the dual string/M-theory picture for strong coupling. In particular, we observe the confined phase in the BFSS matrix model, which is a nontrivial consequence of the M-theory picture. We suggest that these models provide us with an ideal framework to study the Schwarzschild black hole, M-theory, and furthermore, the parameter region of the phase transition between type IIA superstring theory and M-theory. A detailed study of M-theory via lattice Monte Carlo simulations of the D0-brane matrix model might be doable with much smaller computational resources than previously expected.