We propose a method to describe consistent equations of state (EOS) for arbitrary systems. Complex EOS are traditionally obtained by fitting suitable analytical expressions to thermophysical data. A key aspect of EOS are that the relationships betwee
n state variables are given by derivatives of the system free energy. In this work, we model the free energy with an artificial neural network, and utilize automatic differentiation to directly learn to the derivatives of the free energy on two different data sets, the van der Waals system, and published data for the Lennard-Jones fluid. We show that this method is advantageous over direct learning of thermodynamic properties (i.e. not as derivatives of the free energy, but as independent properties), in terms of both accuracy and the exact preservation of the Maxwell relations. Furthermore, the method can implicitly solve the integration problem of computing the free energy of a system without explicit integration.
We study a spin-ice Kondo lattice model on a breathing pyrochlore lattice with classical localized spins. The highly efficient kernel polynomial expansion method, together with a classical Monte Carlo method, is employed in order to study the magneti
c phase diagram at four representative values of the number density of itinerant electrons. We tune the breathing mode by varying the hopping ratio -- the ratio of hopping parameters for itinerant electrons along inequivalent paths. Several interesting magnetic phases are stabilized in the phase diagram parameterized by the hopping ratio, Kondo coupling, and electronic filling fraction, including an all-in/all-out ordered spin configuration phase, spin-ice, ordered phases containing $16$ and $32$ spin sites in the magnetic unit cell, as well as a disordered phase at small values of the hopping ratio.
Over the past several years, reliable Quantum Monte Carlo results for the charge density wave transition temperature $T_{cdw}$ of the half-filled two dimensional Holstein model in square and honeycomb lattices have become available for the first time
. Exploiting the further development of numerical methodology, here we present results in three dimensions, which are made possible through the use of Langevin evolution of the quantum phonon degrees of freedom. In addition to determining $T_{cdw}$ from the scaling of the charge correlations, we also examine the nature of charge order at general wave vectors for different temperatures, couplings, and phonon frequencies, and the behavior of the spectral function and specific heat.
Complex behavior poses challenges in extracting models from experiment. An example is spin liquid formation in frustrated magnets like Dy$_2$Ti$_2$O$_7$. Understanding has been hindered by issues including disorder, glass formation, and interpretatio
n of scattering data. Here, we use a novel automated capability to extract model Hamiltonians from data, and to identify different magnetic regimes. This involves training an autoencoder to learn a compressed representation of three-dimensional diffuse scattering, over a wide range of spin Hamiltonians. The autoencoder finds optimal matches according to scattering and heat capacity data and provides confidence intervals. Validation tests indicate that our optimal Hamiltonian accurately predicts temperature and field dependence of both magnetic structure and magnetization, as well as glass formation and irreversibility in Dy$_2$Ti$_2$O$_7$. The autoencoder can also categorize different magnetic behaviors and eliminate background noise and artifacts in raw data. Our methodology is readily applicable to other materials and types of scattering problems.
Electrostatic interactions play an important role in numerous self-assembly phenomena, including colloidal aggregation. Although colloids typically have a dielectric constant that differs from the surrounding solvent, the effective interactions that
arise from inhomogeneous polarization charge distributions are generally neglected in theoretical and computational studies. We introduce an efficient technique to resolve polarization charges in dynamical dielectric geometries, and demonstrate that dielectric effects emph{qualitatively} alter the predicted self-assembled structures, with surprising colloidal strings arising from many-body effects.
Electrostatic interactions between dielectric objects are complex and of a many-body nature, owing to induced surface bound charge. We present a collection of techniques to simulate dynamical dielectric objects. We calculate the surface bound charge
from a matrix equation using the Generalized Minimal Residue method (GMRES). Empirically, we find that GMRES converges very quickly. Indeed, our detailed analysis suggests that the relevant matrix has a very compact spectrum for all non-degenerate dielectric geometries. Each GMRES iteration can be evaluated using a fast Ewald solver with cost that scales linearly or near-linearly in the number of surface charge elements. We analyze several previously proposed methods for calculating the bound charge, and show that our approach compares favorably.
In this paper we present a study of the early stages of unstable state evolution of systems with spatial symmetry changes. In contrast to the early time linear theory of unstable evolution described by Cahn, Hilliard, and Cook, we develop a generaliz
ed theory that predicts two distinct stages of the early evolution for symmetry breaking phase transitions. In the first stage the dynamics is dominated by symmetry preserving evolution. In the second stage, which shares some characteristics with the Cahn-Hilliard-Cook theory, noise driven fluctuations break the symmetry of the initial phase on a time scale which is large compared to the first stage for systems with long interaction ranges. To test the theory we present the results of numerical simulations of the initial evolution of a long-range antiferromagnetic Ising model quenched into an unstable region. We investigate two types of symmetry breaking transitions in this system: disorder-to-order and order-to-order transitions. For the order-to-order case, the Fourier modes evolve as a linear combination of exponentially growing or decaying terms with different time scales.
We extend the early time ordering theory of Cahn, Hilliard, and Cook (CHC) so that our generalized theory applies to solid-to-solid transitions. Our theory involves spatial symmetry breaking (the initial phase contains a symmetry not present in the
final phase). The predictions of our generalization differ from those of the CHC theory in two important ways: exponential growth does not begin immediately following the quench, and the objects that grow exponentially are not necessarily Fourier modes. Our theory is consistent with simulation results for the long-range antiferromagnetic Ising model.
We investigate the approach to stable and metastable equilibrium in Ising models using a cluster representation. The distribution of nucleation times is determined using the Metropolis algorithm and the corresponding $phi^{4}$ model using Langevin dy
namics. We find that the nucleation rate is suppressed at early times even after global variables such as the magnetization and energy have apparently reached their time independent values. The mean number of clusters whose size is comparable to the size of the nucleating droplet becomes time independent at about the same time that the nucleation rate reaches its constant value. We also find subtle structural differences between the nucleating droplets formed before and after apparent metastable equilibrium has been established.
