Nonzero External Field Research Articles

Perfect sampling of $q$-spin systems on $\mathbb{Z}^{2}$ via weak spatial mixing

We present a perfect marginal sampler of the unique Gibbs measure of a spin system on \mathbb{Z}^{2} . The algorithm is an adaptation of a previous “lazy depth-first” approach by the authors, but relaxes the requirement of strong spatial mixing to weak. Our result is a step towards methods of efficient sampling using only weak spatial mixing. The work exploits a classical result in statistical physics relating weak spatial mixing on \mathbb{Z}^{2} to strong spatial mixing on squares. When the spin system exhibits weak spatial mixing, the run-time of our sampler is linear in the size of sample. Applications of note are the ferromagnetic Potts model at supercritical temperatures and the ferromagnetic Ising model with consistent non-zero external field at any non-zero temperature.

Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics

We consider the ferromagnetic q-state Potts model on a finite grid graph with non-zero external field and periodic boundary conditions. The system evolves according to Glauber-type dynamics described by the Metropolis algorithm, and we focus on the low temperature asymptotic regime. We analyze the case of positive external magnetic field associated to one spin value. In this energy landscape there is one stable configuration and q−1 metastable states. We study the asymptotic behavior of the first hitting time from any metastable state to the stable configuration as β→∞ in probability, in expectation, and in distribution. We also identify the exponent of the mixing time and find an upper and a lower bound for the spectral gap. Finally, we identify all the minimal gates and the tube of typical trajectories for the transition from any metastable state to the unique stable configuration by giving a geometric characterization.

Metastability for the degenerate Potts model with negative external magnetic field under Glauber dynamics

We consider the ferromagnetic q-state Potts model on a finite grid with a non-zero external field and periodic boundary conditions. The system evolves according to Glauber-type dynamics described by the Metropolis algorithm, and we focus on the low temperature asymptotic regime. We analyze the case of a negative external magnetic field. In this scenario, there are q − 1 stable configurations and a unique metastable state. We describe the asymptotic behavior of the first hitting time from the metastable state to the set of the stable states as β → ∞ in probability, in expectation, and in distribution. We also identify the exponent of the mixing time and find an upper bound and a lower bound for the spectral gap. We identify the minimal gates for the transition from the metastable state to the set of the stable states and for the transition from the metastable state to a fixed stable state. Furthermore, we identify the tube of typical trajectories for these two transitions. The detailed description of the energy landscape that we develop allows us to give precise asymptotics for the expected transition time from the unique metastable state to the set of the stable configurations.

Uranium Going the Soft Way: Low-Valent Uranium(III) Coordinated to an Arene-Anchored Tris-Thiophenolate Ligand.

The synthesis of a tripodal, S-based ligand, namely the mesitylene-anchored, tris-thiophenolate-functionalized (mes(Me,AdArS)3)3- (1)3-, and its coordination chemistry with low-valent uranium to form [UIII((SArAd,Me)3mes)] (1-U) are reported. Single-crystal X-ray diffraction analysis reveals a C3-symmetric molecular structure. Full characterization of 1-U was performed using nuclear magnetic resonance, UV-vis-NIR electronic absorption, and electron paramagnetic resonance spectroscopies as well as SQUID magnetometry, thus confirming the U(III) oxidation state. Alternating current magnetic studies show that 1-U exhibits single-molecule magnet behavior at low temperatures in a non-zero external field. Comparison of these results to those of the previously reported mesitylene-anchored complexes, [UIII((OArAd,Me)3mes)] and [UIII((OArtBu,tBu)3mes)], indicates a drastic change in the electronic structure when moving from phenolate-based ligands to thiophenolate-based 1, which is further discussed by means of computational analysis (NBO, DFT, and QTAIM). Despite the U-O bonds being stronger, a much higher covalency was found for the U-S analogue.

Electrical and magnetic properties of amorphous Fe22.5Co22.5Ni22.5Cr22.5Zr10 alloy

This report is focused on the investigation of electrical and magnetic properties of distorted bcc system. The inspiration for the selection of amorphous Fe22.5Co22.5Ni22.5Cr22.5Zr10 alloy with a distorted bcc structure is based on the theoretical band calculation. It is confirmed that the free electron density of state of disordered bcc FeNiCr alloy increases at Fermi surface.Amorphous Fe22.5Co22.5Ni22.5Cr22.5Zr10 alloy, hereafter denoted as a-FeCoNiCrZr, shows among all the metallic materials the weakest temperature dependence of the electrical resistivity, ρ0(T). The weak ρ0(T) has been interpreted in the context of different physical processes such as tunnelling of free electrons and electron phonon interactions.Magnetically, a-FeCoNiCrZr consists of independent soft ferromagnetic clusters with average cluster size of about 1840 atoms. The Curie temperature, TC, was verified using Landau’s theory of second-order phase transitions in low non-zero external fields. The reduced magnetization, M(T)/M(0), as a function of reduced temperature, T/TC, is explained in the framework of the exchange integral fluctuation theory. The exchange integral fluctuation is dominant only at low external fields. At Bex = 9 T, the exchange integral fluctuation has no noticeable effect on reduced magnetization. At Bex = 9 T, the precision of magnetic clusters around the Bex controls the behaviour of reduced magnetization as function of temperature.

Modifying the transition temperature, 120\u2009K\u2009\u2264\u2009Tc\u2009\u2264\u20091150\u2009K, of amorphous Fe90\u2212xCoxSc10 with simultaneous alteration of fluctuation of exchange integral up to zero

Amorphous (a-) Fe90−xCoxSc10 alloys have been produced by rapid quenching from the melt. The Curie temperature, TC, was determined using both mean field theory and Landau’s theory of second-order phase transitions in zero and non-zero external fields. The dependence of TC on the atomic spacing can be explained by the empirical Bethe-Slater curve. The value of TC of a- Fe5Co85Sc10, determined by the above theoretical approaches is 1150 K, which is the highest TC ever measured for amorphous alloys. The flattening of the measured normalized magnetization, M(T)/M(0), as a function of the reduced temperature, T/TC, is explained within the framework of the Handrich- Kobe model. According to this model the fluctuation of the exchange integral is the main reason for the flattening of M(T)/M(0). In the case of a-Fe90Sc10 without Co, however, the fluctuation of the exchange integral is dominant only at zero external field, Bex = 0. At Bex = 9 T, however, the fluctuation of the exchange integral has no conspicuous effect on the reduction of the magnetization. It is shown that at Bex = 9 T the frozen magnetic clusters control the behaviour of the reduced magnetization as function of T/TC. In contrast to other ferromagnetic alloys, where the flattening of M(T)/M(0) is characteristic for an amorphous structure, the a- Fe5Co85Sc10 does not exhibit any trace of the fluctuation of the exchange integral.

Frequency band gaps in dielectric granular metamaterials modulated by electric field

Wave propagation in granular materials is known to be dispersive. Micromorphic continuum model based upon granular micromechanics (Misra, A. and P. Poorsolhjouy, Continuum Mech. Thermodyn, 2016. 28(1-2): p. 215-234.) has the ability to describe this dispersion behavior. In this paper we show that the dispersive behavior can be modulated by using electric field when the grains have dielectric properties. To this end, we apply the recently enhanced model that incorporates electro-elastic coupling by connecting microstrain to electric dipole and quadrupole densities due to bound charges in dielectric grains (Romeo, M., Mech. Res. Commun., 2018. 91: p. 33-38.). We particularly investigate the effect of induced polarization that arises due to an imposed electric field. Two cases of dielectric one dimensional infinite rods with the same micromorphic properties have been studied, where case 1 and 2 are in null and nonzero external electric fields, respectively. Parametric studies are performed to understand the contribution of the polarizability (dipole effect), intrinsic quadrupole density, and external electric field on the dispersive behavior of granular media. Results predict an acoustic and an optical branch in the dispersive curve. Polarizability and external electric field are mainly affecting small wavenumber behavior of the wave branches, while quadrupole density alters the behavior of the material at large wavenumbers. A possibility of altering the optical branch to an acoustic branch is also observed, for which instability or attenuation occurs depending upon the direction of the imposed electric field with respect to the wave propagation direction. We find that the location and the width of the frequency band gaps can be altered using external electric field. The possibility of creating or removing frequency band gaps is also shown to exist. The extended theory accounting for electro-elasticity can therefore be utilized as a tool to analyze existing granular media, or to design granular metamaterials, as it systematizes the design process and eliminates ad-hoc manners leading to large data libraries.

Stability of the Uniqueness Regime for Ferromagnetic Glauber Dynamics Under Non-reversible Perturbations

We prove a general stability property concerning finite-range, attractive interacting particle systems on $$\{-\,1, 1\}^{{\mathbb {Z}}^d}$$ . If the particle system has a unique stationary measure and, in a precise sense, relaxes to this stationary measure at an exponential rate, then any small perturbation of the dynamics also has a unique stationary measure to which it relaxes at an exponential rate. To apply this result, we study the particular case of Glauber dynamics for the Ising model. We show that for any nonzero external field the dynamics converges to its unique invariant measure at an exponential rate. Previously, this was only known for $$\beta <\beta _c$$ and $$\beta $$ sufficiently large. As a consequence of our stability property, we then conclude that Glauber dynamics for the Ising model is stable to small, non-reversible perturbations in the entire uniqueness phase, excluding only the critical point.

The Potts Model on a Bethe Lattice in an External Field

A solution for the Potts model with arbitrary number of states on a Bethe lattice in a nonzero external field has been obtained. A line of first-order phase transitions has been constructed in the temperature – external-field plane, terminating at the point of the second-order phase transition. The magnitude of the magnetization jump on the phase-transition lines has been found, as well as some of the critical exponents characterizing this phase transition.

Phase transition properties for the spatial public goods game with self-questioning mechanism

The spatial public goods game is one of the most popular models for studying the emergence and maintenance of cooperation among selfish individuals. A public goods game with costly punishment and self-questioning updating mechanism is studied in this paper. The theoretical analysis and Monte Carlo simulation are involved to analyze this model. This game model can be transformed into Ising model with an external field by theoretical analysis. When the costly punishment exists, the effective Hamiltonian includes the nearest-, the next-nearest-and the third-nearest-neighbor interactions and non-zero external field. The interactions are only determined by costly punishment. The sign of the interaction is always greater than zero, so it has the properties of ferromagnetic Ising. The external field is determined by the factor r of the public goods game, the fine F on each defector within the group, and the relevant punishment cost C. The Monte Carlo simulation results are consistent with the theoretical analysis results. In addition, the phase transitions and critical behaviors of the public goods game are also studied using the finite size scaling theory. The results show that the discontinuous phase transition has the same finite size effects as the two-dimensional Ising model, but the continuous phase transitions is inconsistent with Ising model.

Space-and-time current spectroscopy of a β-Ga₂O₃ crystal.

We report the excitation of the non-steady-state photoelectro-motive force in a monoclinic gallium oxide crystal. The crystal grown in an oxygen atmosphere is insulating and highly transparent for a visible light, nevertheless, the formation of dynamic space-charge gratings and observation of the photo-EMF signal is achieved under the laser illumination with wavelength λ = 532 nm. The induced ac current is studied for the cases of zero and non-zero external electric fields, which imply the non-resonant and resonant mechanisms of space-charge recording. The dependencies of the signal amplitude versus the frequency of phase modulation, light intensity, spatial frequency, light polarization and value of the external dc electric field are measured. The material demonstrates the anisotropy along the [100] and [010] directions, namely, there is a weak difference of the transport parameters and a pronounced polarization dependence of the signal. The photoconductivity and diffusion length of electrons are estimated for the chosen light wavelength.

Effective ergodicity in single-spin-flip dynamics.

A quantitative measure of convergence to effective ergodicity, the Thirumalai-Mountain (TM) metric, is applied to Metropolis and Glauber single-spin-flip dynamics. In computing this measure, finite lattice ensemble averages are obtained using the exact solution for a one dimensional Ising model, whereas the time averages are computed with Monte Carlo simulations. The time evolution of the effective ergodic convergence of Ising magnetization is monitored. By this approach, diffusion regimes of the effective ergodic convergence of magnetization are identified for different lattice sizes, nonzero temperature, and nonzero external field values. Results show that caution should be taken when using the TM metric at system parameters that give rise to strong correlations.

Nonstationary holographic currents in neutron-irradiated SiC crystal

We report the excitation of nonstationary holographic currents in semi-insulating 6H-SiC crystal preliminarily irradiated by reactor neutrons. The currents are studied for the cases of zero and non-zero external electric fields. The dependences of the signal amplitude versus the frequency of phase modulation, light intensity, spatial frequency and amplitude of the external ac field are measured. The frequency transfer functions of the effect demonstrate unusual behaviour, namely, there are two frequency-independent regions in the diffusion regime of signal excitation and low-frequency maximum in the experiments with the applied ac field. These peculiarities are explained in the frames of a two-level model of semiconductor. Photoconductivity, diffusion length of electrons, thermal excitation rate and ionization cross section for shallow traps are estimated for the wavelength λ = 532 nm.

Approximation Algorithms for Two-State Anti-Ferromagnetic Spin Systems on Bounded Degree Graphs

We show that for the anti-ferromagnetic Ising model on the Bethe lattice, weak spatial mixing implies strong spatial mixing. As a by-product of our analysis, we obtain what is to the best of our knowledge the first rigorous proof of the uniqueness threshold for the anti-ferromagnetic Ising model (with non-zero external field) on the Bethe lattice. Following a method due to Weitz [15], we then use the equivalence between weak and strong spatial mixing to give a deterministic fully polynomial time approximation scheme for the partition function of the anti-ferromagnetic Ising model with arbitrary field on graphs of degree at most $$d$$ , throughout the uniqueness region of the Gibbs measure on the infinite $$d$$ -regular tree. By a standard correspondence, our results translate to arbitrary two-state anti-ferromagnetic spin systems with soft constraints. Subsequent to a preliminary version of this paper, Sly and Sun [13] have shown that our results are optimal in the sense that, under standard complexity theoretic assumptions, there does not exist a fully polynomial time approximation scheme for the partition function of such spin systems on graphs of maximum degree $$d$$ for parameters outside the uniqueness region. Taken together, the results of [13] and of this paper therefore indicate a tight relationship between complexity theory and phase transition phenomena in two-state anti-ferromagnetic spin systems.

Bounds on convergence for the empirical vector of the Curie–Weiss–Potts model with a non-zero external field vector

Abstract In the present paper we obtain rates of convergence for limit theorems via Stein’s Method of exchangeable pairs in the context of the Curie–Weiss–Potts model and we consider only the case of non-zero external field h ∈ R q . Our interest is in the limit distribution of the empirical vector of the spin variables and we obtain bounds for multivariate normal approximation.

Periodic Gibbs measures for the Potts model on the Cayley tree

We study the Potts model on the Cayley tree. We demonstrate that for this model with a zero external field, periodic Gibbs measures on some invariant sets are translation invariant. Furthermore, we find the conditions under which the Potts model with a nonzero external field admits periodic Gibbs measures.

A study of critical phenomena and dissipative nanostructures in self-organizing polymer systems

A research methodology based on scaling concepts is developed in detail for nonequilibrium polymer systems. Melt-crystallized linear high-density polyethylene is chosen as an example. In flexible-chain semicrystalline polymers, the transition from a solid isotropic or oriented state to a melt or from a solid isotropic state to an oriented state below the critical degree of polymerization occurs through necking at a nonzero external field on the combined line of first- and second-order phase transitions. A melt is a symmetric phase with a zero order parameter. Lamellar and fibrillar semicrystalline phases are phases with inherent order parameters that are periodic functions of one coordinate, and the neck draw ratio is another order parameter. At the critical degree of polymerization, all the phases are identical. In terms of the fluctuation theory of phase transitions and critical phenomena, the quantitative dependence of macroscopic properties on nanostructure parameters in this polymer material is revealed. The neck draw ratio and the draw ratio at break are macroscopic properties. The structure is characterized by the average thickness of amorphous layers. The square of the neck draw ratio is equal to the product of the square of the draw ratio at break and the probability of collision of chain ends. In turn, this probability is proportional to the average thickness of amorphous layers in an isotropic sample. The problems of dynamic scaling and entanglements are discussed.

On phase transitions of the Potts model with three competing interactions on Cayley tree

In the present paper we study a phase transition problem for the Potts model with three competing interactions, the nearest neighbors, the second neighbors and triples of neighbors and non-zero external field on Cayley tree of order two. We prove that for some parameter values of the model there is phase transition. We reduce the problem of describing by limiting Gibbs measures to the problem of solving a system of nonlinear functional equations. We extend the results obtained by Ganikhodjaev and Rozikov [Math. Phys. Anal. Geom., 2009, 12, No. 2, 141-156] on phase transition for the Ising model to the Potts model setting.

Central Limit Theorems for the Energy Density in the Sherrington-Kirkpatrick Model

In this paper we consider central limit theorems for various macroscopic observables in the high temperature region of the Sherrington-Kirkpatrick spin glass model. With a particular focus on obtaining a quenched central limit theorem for the energy density of the system with non-zero external field, we show how to combine the mean field cavity method with Stein's method in the quenched regime. The result for the energy density extends the corresponding result of Comets-Neveu.

Euclidean Gibbs Measures of Interacting Quantum Anharmonic Oscillators

A rigorous description of the equilibrium thermodynamic properties of an infinite system of interacting $\nu$-dimensional quantum anharmonic oscillators is given. The oscillators are indexed by the elements of a countable set $\mathbb{L}\subset \mathbb{R}^d$, possibly irregular; the anharmonic potentials vary from site to site. The description is based on the representation of the Gibbs states in terms of path measures -- the so called Euclidean Gibbs measures. It is proven that: (a) the set of such measures $\mathcal{G}^{\rm t}$ is non-void and compact; (b) every $\mu \in \mathcal{G}^{\rm t}$ obeys an exponential integrability estimate, the same for the whole set $\mathcal{G}^{\rm t}$; (c) every $\mu \in \mathcal{G}^{\rm t}$ has a Lebowitz-Presutti type support; (d) $\mathcal{G}^{\rm t}$ is a singleton at high temperatures. In the case of attractive interaction and $\nu=1$ we prove that $|\mathcal{G}^{\rm t}|>1$ at low temperatures. The uniqueness of Gibbs measures due to quantum effects and at a nonzero external field are also proven in this case. Thereby, a qualitative theory of phase transitions and quantum effects, which interprets most important experimental data known for the corresponding physical objects, is developed. The mathematical result of the paper is a complete description of the set $\mathcal{G}^{\rm t}$, which refines and extends the results known for models of this type.