Lattice Model Study Research Articles

Influence of ion structure and solvent electric dipole on ultrananoporous supercapacitor: a lattice model study

A five-state modified BEG model is proposed for describing electrolyte in polar solvent in cylindrical electrode pore in which only one row of particles can be stationed. Two properties the closest to the actual situation of the aqueous electrolyte are integrated into the model: cation is dimer comprised of two tangentially tethered hard spheres of different diameters: one is charged, while the other is neutral, and polar solvent is modeled as neutral hard sphere with an electric dipole. The system partition function is obtained by numerically solving maximum real root of characteristic equation of Kramers-Wannier transfer matrix. The model is used to investigate effects of ion structure and electric valence, solvent electric dipole, and cylindrical pore radius on specific differential capacitance and specific energy storage of the resulting supercapacitor. Main findings are briefly described below. (i) The dimer counter-ion electric valence does not exert obvious influence on the saturation value of the but reduces the threshold electrode potential strength beyond which the value is just reached. (ii) Whether the dimer counter-ion is monovalent or bivalent, the peak height and the value tend to rise with the dimer neutral site size decreasing, but influence of the value on the value is very small. Only when the value is small enough, the value rises a little with decrease of the value. (iii) Increase of solvent electric dipole moment (whether by increasing the dipole charge or dipole length) always raises the value, and enlarges width of the pure solvent domain or zero and zero domain around the zero electrode potential, but does not change the value obviously. (iv) With the pore size increasing, the value reduces and the value increases. So, using small size pore is favorable to improve the supercapacitor performance from the perspective of energy storage and electrode potential applied. (v) The three parameters: dipole charge, and dipole length, are cooperative in influencing the value.

Critical temperature and magnetic properties of new 2D lattice model with double hexagonal symmetry: Monte Carlo study

Here, we present a theoretical study of a new statistical lattice model based on a double hexagonal structure associated with G2 symmetry. Using Monte Carlo simulation, we study the magnetic properties of the Ising-1/2 model with spin values σ = ±1 residing on the sites of our double hexagonal lattice. In particular, we calculate and analyze the thermal behavior of the total and partial magnetizations as well as the corresponding susceptibilities for different lattice sizes. The present study shows that the total and partial magnetizations vanish at the same critical temperature. This vanishing is continuous, indicating that the type of the transition is a second order. With the help of the finite-size scaling analysis, we estimate the critical transition temperature related to the uniform coupling interaction value equals one. Our findings reflect a good estimation of the critical temperature, TC that is equal to 2.976∓0.004JkB. The obtained critical temperature of our presented model can be found between the critical temperatures of hexagonal and triangular lattice models.

Partition-function-zero analysis of polymer adsorption for a continuum chain model

Polymer chains undergoing adsorption are expected to show universal critical behavior which may be investigated using partition function zeros. The focus of this work is the adsorption transition for a continuum chain, allowing for investigation of a continuous range of the attractive interaction and comparison with recent high-precision lattice model studies. The partition function (Fisher) zeros for a tangent-hard-sphere N-mer chain (monomer diameter σ) tethered to a flat wall with an attractive square-well potential (range λσ, depth ε) have been computed for chains up to N=1280 with 0.01≤λ≤2.0. In the complex-Boltzmann-factor plane these zeros are concentrated in an annular region, centered on the origin and open about the real axis. With increasing N, the leading zeros, w_{1}(N), approach the positive real axis as described by the asymptotic scaling law w_{1}(N)-y_{c}∼N^{-ϕ}, where y_{c}=e^{ε/k_{B}T_{c}} is the critical point and T_{c} is the critical temperature. In this work, we study the polymer adsorption transition by analyzing the trajectory of the leading zeros as they approach y_{c} in the complex plane. We use finite-size scaling (including corrections to scaling) to determine the critical point and the scaling exponent ϕ as well as the approach angle θ_{c}, between the real axis and the leading-zero trajectory. Variation of the interaction range λ moves the critical point, such that T_{c} decreases with λ, while the results for ϕ and θ_{c} are approximately independent of λ. Our values of ϕ=0.479(9) and θ_{c}=56.8(1.4)^{∘} are in agreement with the best lattice model results for polymer adsorption, further demonstrating the universality of these constants across both lattice and continuum models.

Large heat-capacity jump in cooling-heating of fragile glass from kinetic Monte Carlo simulations based on a two-state picture.

The specific-heat capacity c_{v} of glass formers undergoes a hysteresis when subjected to a cooling-heating cycle, with a larger c_{v} and a more pronounced hysteresis for fragile glasses than for strong ones. Here we show that these experimental features, including the unusually large magnitude of c_{v} of fragile glasses, are well reproduced by kinetic Monte Carlo and equilibrium study of a distinguishable particle lattice model incorporating a two-state picture of particle interactions. The large c_{v} in fragile glasses is caused by a dramatic transfer of probabilistic weight from high-energy particle interactions to low-energy ones as temperature decreases.

Magnetic correlations in the triangular antiferromagnet FeGa2S4

The crystal structure and magnetic correlations in triangular antiferromagnet FeGa$_2$S$_4$ are studied by x-ray diffraction, magnetic susceptibility, neutron diffraction and neutron inelastic scattering. We report significant mixing at the cation sites and disentangle magnetic properties dominated by major and minor magnetic sites. The magnetic short-range correlations at 0.77 \AA$^{-1}$ correspond to the major sites and being static at base temperature they evolve into dynamic correlations around 30 - 50 K. The minor sites contribute to the magnetic peak at 0.6 \AA$^{-1}$, which vanishes at 5.5 K. Our analytical studies of triangular lattice models with bilinear and biquadratic terms provide the ratios between exchanges for the proposed ordering vectors. The modelling of the inelastic neutron spectrum within linear spin wave theory results in the set of exchange couplings $J_1=1.7$\,meV, $J_2=0.9$\,meV, $J_3=0.8$\,meV for the bilinear Heisenberg Hamiltonian. However, not all features of the excitation spectrum are explained with this model.

Study of Topological Lattice Models with Synthetic Dimensions

Study of Topological Lattice Models with Synthetic Dimensions

Study of Simulation Cell Size in Mean-Field Studies of Interacting Lattice Models

Study of Simulation Cell Size in Mean-Field Studies of Interacting Lattice Models

Gō model revisited.

This review discusses Gō models broadly used in biomolecular simulations. I start with a brief description of the original lattice model study by Nobuhiro Gō. Then, the theory of protein folding behind Gō model, free energy approaches, and off-lattice Gō models are reviewed. I also mention a stringent test for the assumption in Gō models given from all-atom molecular dynamics simulations. Subsequently, I move to application of Gō models to protein dynamical functions. Various extension of Gō models is also reviewed. Finally, some publicly available tools to use Gō models are listed.

Active and passive transport of cargo in a corrugated channel: A lattice model study.

Inside cells, cargos such as vesicles and organelles are transported by molecular motors to their correct locations via active motion on cytoskeletal tracks and passive, Brownian diffusion. During the transportation of cargos, motor-cargo complexes (MCCs) navigate the confining and crowded environment of the cytoskeletal network and other macromolecules. Motivated by this, we study a minimal two-state model of motor-driven cargo transport in confinement and predict transport properties that can be tested in experiments. We assume that the motion of the MCC is directly affected by the entropic barrier due to confinement if it is in the passive, unbound state but not in the active, bound state where it moves with a constant bound velocity. We construct a lattice model based on a Fokker Planck description of the two-state system, study it using a kinetic Monte Carlo method and compare our numerical results with analytical expressions for a mean field limit. We find that the effect of confinement strongly depends on the bound velocity and the binding kinetics of the MCC. Confinement effectively reduces the effective diffusivity and average velocity, except when it results in an enhanced average binding rate and thereby leads to a larger average velocity than when unconfined.

Characterization of $\mathcal{B} (\infty)$ using marginally large tableaux and rigged configurations in the $A_n$ case via integer sequences

Rigged configurations are combinatorial objects prominent in the study of solvable lattice models. Marginally large tableaux are semi-standard Young tableaux of special form that give a realization of the crystals ${\cal B}(\infty)$. We introduce cascading sequences to characterize marginally large tableaux. Then we use cascading sequences and a non-explicit crystal isomorphism between marginally large tableaux and rigged configurations to give a characterization of the latter set, and to give an explicit bijection between the two sets.

Order-disorder transition in active nematic: A lattice model study

We introduce a lattice model for active nematic composed of self-propelled apolar particles, study its different ordering states in the density-temperature parameter space, and compare with the corresponding equilibrium model. The active particles interact with their neighbours within the framework of the Lebwohl-Lasher model, and move anisotropically along their orientation to an unoccupied nearest neighbour lattice site. An interplay of the activity, thermal fluctuations and density gives rise distinct states in the system. For a fixed temperature, the active nematic shows a disordered isotropic state, a locally ordered inhomogeneous mixed state, and bistability between the inhomogeneous mixed and a homogeneous globally ordered state in different density regime. In the low temperature regime, the isotropic to the inhomogeneous mixed state transition occurs with a jump in the order parameter at a density less than the corresponding equilibrium disorder-order transition density. Our analytical calculations justify the shift in the transition density and the jump in the order parameter. We construct the phase diagram of the active nematic in the density-temperature plane.

Mean field study of a propagation-turnover lattice model for the dynamics of histone marking

We present a mean field study of a propagation-turnover lattice model, which was proposed by Hodges and Crabtree [Proc. Nat. Acad. Sci. 109, 13296 (2012)] for understanding how posttranslational histone marks modulate gene expression in mammalian cells. The kinetics of the lattice model consists of nucleation, propagation and turnover mechanisms, and exhibits second-order phase transition for the histone marking domain. We showed rigorously that the dynamics essentially depends on a non-dimensional parameter κ = k +/k −, the ratio between the propagation and turnover rates, which has been observed in the simulations. We then studied the lowest order mean field approximation, and observed the phase transition with an analytically obtained critical parameter. The boundary layer analysis was utilized to investigate the structure of the decay profile of the mark density. We also studied the higher order mean field approximation to achieve sharper estimate of the critical transition parameter and more detailed features. The comparison between the simulation and theoretical results shows the validity of our theory.

Computer simulation study of a mesogenic lattice model based on long-range dispersion interactions.

In contrast to thermotropic biaxial nematic phases, for which some long sought for experimental realizations have been obtained, no experimental realizations are yet known for their tetrahedratic and cubatic counterparts, involving orientational orders of ranks 3 and 4, respectively, also studied theoretically over the last few decades. In previous studies, cubatic order has been found for hard-core or continuous models consisting of particles possessing cubic or nearly cubic tetragonal or orthorhombic symmetries; in a few cases, hard-core models involving uniaxial (D_{∞h}-symmetric) particles have been claimed to produce cubatic order as well. Here we address by Monte Carlo simulation a lattice model consisting of uniaxial particles coupled by long-range dispersion interactions of the London-De Boer-Heller type; the model was found to produce no second-rank nematic but only fourth-rank cubatic order, in contrast to the nematic behavior long known for its counterpart with interactions truncated at nearest-neighbor separation.

Solving lattice density functionals close to the Mott regime

We study a lattice version of the local density approximation (LDA) based on Behte ansatz (BALDA). Contrary to what happens in Density Functional Theory (DFT) in the continuum and despite its name, BALDA displays some very non-local features and it has a discontinuous functional derivative. The same features prevent the convergence of the self-consistent Kohn-Sham cycle thus hindering the study of BALDA solutions close to a Mott phase or in the Coulomb blockade regime. Here we propose a numerical approach which, differently from previous works, does not introduce ad hoc parameters to smear out the singularity. Our results are relevant for all lattice models where BALDA is applied ranging from Kondo systems to harmonically trapped Hubbard fermions. As an example we apply the method to the study of a one-dimensional lattice model with Hubbard interaction and a staggered potential which can be driven from an ionic to a Mott insulating state. In the Mott regime the presence of a "vacuum" allows us to calculate the different contribution to the gap and to highlight an ultranonlocality of BALDA.

Phonon interference and thermal conductance reduction in atomic-scale metamaterials

We introduce and model a three-dimensional (3D) atomic-scale phononic metamaterial producing two-path phonon interference antiresonances to control the heat flux spectrum. We show that a crystal plane partially embedded with defect-atom arrays can completely reflect phonons at the frequency prescribed by masses and interaction forces. We emphasize the predominant role of the second phonon path and destructive interference in the origin of the total phonon reflection and thermal conductance reduction in comparison with the Fano-resonance concept. The random defect distribution in the plane and the anharmonicity of atom bonds do not deteriorate the antiresonance. The width of the antiresonance dip can provide a measure of the coherence length of the phonon wave packet. All our conclusions are confirmed both by analytical studies of the equivalent quasi-1D lattice models and by numerical molecular dynamics simulations of realistic 3D lattices.

Wake-mediated interaction between driven particles crossing a perpendicular flow

Diagonal or chevron patterns are known to spontaneously emerge at the intersection of two perpendicular flows of self-propelled particles, e.g. pedestrians. The instability responsible for this pattern formation has been studied in previous work in the context of a mean-field approach. Here, we investigate the microscopic mechanism yielding this pattern. We present a lattice model study of the wake created by a particle crossing a perpendicular flow and show how this wake can localize other particles traveling in the same direction as a result of an effective interaction mediated by the perpendicular flow. The use of a semi-deterministic model allows us to characterize the effective interaction between two particles analytically.

Reflection Relations and Fermionic Basis

There are two approaches to computing the one-point functions for sine-Gordon model in infinite volume. One is based on the use of the reflection relations, this is a bootstrap type procedure. Another is based on using the fermionic basis which originated in the study of lattice model. We show that the two procedures are deeply interrelated.

Cracking of the concrete cover due to reinforcement corrosion: A two-dimensional lattice model study

Corrosion of steel reinforcement is a serious problem for durability and serviceability of reinforced concrete. As the reinforcing steel corrodes, it expands and exerts pressure on the surrounding concrete cover, causing tensile stresses in concrete. This ultimately leads to cracking and spalling of the concrete cover, further exacerbating the durability problems of a structure and increasing the rate of its deterioration. In order to study cracking mechanisms due to reinforcement corrosion, mechanics of the problem was implemented in a two-dimensional lattice model. Heterogeneous nature of concrete was taken into account in the mechanical analysis. Firstly, the case of uniform corrosion was tested, and successfully verified using experimental data from the literature. Also, it was found that cracking pressure is not a deterministic value, and depends on local mechanical parameters. Secondly, two pitting scenarios were tested and compared to the uniform corrosion case. Pitting results in significant reduction of cracking pressure, compared to the uniform corrosion case. Based on the proposed model, some conclusions with implications for engineering practice were drawn.

Computer simulation study of the two-dimensional nematic lattice model based on the modified Gruhn–Hess pair potential model

A modified Gruhn–Hess pair potential model, where the potential parameters related to the elastic constants are different from the original model, was investigated with the aid of Monte Carlo (MC) simulation and Mean Field (MF) theory based upon a two-dimensional nematic lattice model. The model produces a ground state in perfect nematic order, where particles are aligned in the lattice plane. Both the MF predictions and the simulation results for the second-rank ordering tensor show that the system is biaxial in the low-temperature region, with a positive primary order parameter and the main director aligned along the lattice axis. A transition to uniaxial order takes place at higher temperatures with a negative primary order parameter and the director is orthogonal to the lattice plane. This orientational order survives up to temperatures higher than the transition temperature of the three-dimensional lattice model, possibly at all finite temperatures. MF predictions agree qualitatively with simulation but, in quantitative terms, the transition temperature is overestimated by 52%.

Finite size scaling study of lattice models in the three-dimensional Ising universality class

We simulate the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. We perform a finite size scaling study of lattices of a linear size up to L=360 to obtain accurate estimates for critical exponents. We focus on values of D, where the amplitudes of leading corrections are small. Furthermore we employ improved observables that have a small amplitude of the leading correction. We obtain nu=0.63002(10), eta=0.03627(10) and omega=0.832(6). We compare our results with those obtained from previous Monte Carlo simulations and high temperature series expansions of lattice models, by using field theoretic methods and experiments.