Ising model

About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.

First-principles calculations of the phase diagrams of noble metals: Cu-Au, Cu-Ag, and Ag-Au.

Abstract: It is shown how the temperature-composition phase diagrams and thermodynamic properties of noble-metal alloys can be accurately reproduced by solving the three-dimensional nearest-neighbor fcc Ising model with volume-dependent interaction energies determined from the properties of the ordered phases alone. It is found that lattice relaxation effects are essential in determining order-disorder critical temperatures. This approach enables the understanding of phase diagrams in terms of the electronic properties and atomic-scale structure of the constituent ordered phases.

Out-of-equilibrium dynamics with matrix product states

Abstract: Theoretical understanding of strongly correlated systems in one spatial dimension (1D) has been greatly advanced by the density-matrix renormalization group (DMRG) algorithm, which is a variational approach using a class of entanglement-restricted states called matrix product states (MPSs). However, DMRG suffers from inherent accuracy restrictions when multiple states are involved due to multi-state targeting and also the approximate representation of the Hamiltonian and other operators. By formulating the variational approach of DMRG explicitly for MPSs one can avoid errors inherent in the multi-state targeting approach. Furthermore, by using the matrix product operator (MPO) formalism, one can exactly represent the Hamiltonian and other operators relevant for the calculation. The MPO approach allows 1D Hamiltonians to be templated using a small set of finite state automaton (FSA) rules without reference to the particular microscopic degrees of freedom. We present two algorithms which take advantage of these properties: eMPS to find excited states of 1D Hamiltonians and tMPS for the time evolution of a generic time-dependent 1D Hamiltonian. We properly account for time-ordering of the propagator such that the error does not depend on the rate of change of the Hamiltonian. Our algorithms use only the MPO form of the Hamiltonian, and so are applicable to microscopic degrees of freedom of any variety, and do not require Hamiltonian-specialized implementation. We benchmark our algorithms with a case study of the Ising model, where the critical point is located using entanglement measures. We then study the dynamics of this model under a time-dependent quench of the transverse field through the critical point. Finally, we present studies of a dipolar, or long-range Ising model, again using entanglement measures to find the critical point and study the dynamics of a time-dependent quench through the critical point.

Critical and thermodynamic properties of the randomly dilute Ising model

Abstract: The randomly bond-dilute two-dimensional nearest-neighbor Ising model on the square lattice is studied by renormalization-group methods based on the Migdal-Kadanoff approximate recursion relations. Calculations give both thermal and magnetic exponents associated with the percolative fixed point. Differential recursion relations yield a phase diagram which is in quantitative agreement with all known results. Curves for the specific heat, percolation probability, and magnetization are displayed. The critical region of the specific heat becomes unobservably narrow well above the percolation threshold ${p}_{c}$. This provides a possible explanation for the apparent specific-heat rounding in certain experiments.

Domain wall theory for ferroelectric hysteresis

Abstract: This paper addresses the modeling of hysteresis in ferroelectric materials through consideration of domain wall bending and translation. The development is considered in two steps. First, dielectric constitutive relations are obtained through consideration of Langevin, Ising spin and preferred orientation theories with domain interactions incorporated through mean field relations. This yields a model for the anhysteretic polarization that occurs in the absence of domain wall pinning. Second, hysteresis is incorporated through the consideration of domain wall dynamics and the quantification of energy losses due to inherent inclusions or pinning sites within the material. This yields a model analogous to that developed by Jiles and Atherton for ferromagnetic materials. The viability of the model is illustrated through comparison with experimental data from a PMN-PT-BT actuator operating at a temperature within the ferroelectric regime.

Dynamics of Nucleation in the Ising Model

Abstract: Reactive pathways to nucleation in a three-dimensional Ising model at 60% of the critical temperature are studied using transition path sampling of single spin flip Monte Carlo dynamics. Analysis of the transition state ensemble (TSE) indicates that the critical nuclei are rough and anisotropic. The TSE, projected onto the free energy surface characterized by cluster size, N, and surface area, S, indicates the significance of other variables in addition to these two traditional reaction coordinates for nucleation. The transmission coefficient along N is ~ 0.35, and this reduction of the transmission coefficient from unity is explained in terms of the stochastic nature of the dynamic model.