Magnetic Phase Transitions in Quantum Ising Model with Annealed Antiferromagnetic Bond Randomness

The effect of annealed antiferromagnetic bond randomness on the phase transitions of the Quantum Ising Model (QIM) is studied by using mean-field renormalization group method. It is argued that bond randomness drastically alters multicritical phase diagram via transverse field. Multicritical points and coexistence region of ferromagnetic and antiferromagnetic case exist only at weak transverse field,.and are entirely eliminated at strong transverse field. The coexistence region diminishes in reducing the fluctuation interaction. This physical picture demonstrates that the competition between transverse field and exchange interaction and fluctuation interaction via bond randomness play an important role in generating multiphase structure. Another consequence of competition is that tricritical points of first-second order phase transitions are not entirely eliminated by bond randomness in two-dimensional QIM.     

The Critical Behavior of the Antiferromagnetic Ising Model with Long-Range Interaction Effects

In this paper, the antiferromagnetic Ising model with ferromagnetic long-range interaction is modeled by the Monte Carlo method. The case of ferromagnetic long-range forces decreasing by a power law is considered. The dependence of the phase-transition temperature on long-range interaction parameters is obtained. The phase diagram was constructed at different values of long-range interaction parameters. Conditions for the existence of the frustrated state of the system were revealed.     

一维钻石链反铁磁Ising模型磁化的模拟

采用Monte Carlo模拟方法对自旋为1/2的一维钻石链反铁磁Ising系统的磁化行为进行研究.在这个系统中,反铁磁的交换作用和三角结构导致存在自旋阻挫.重点研究不同的反铁磁自旋交换作用对系统磁行为和自旋构型的影响.模拟磁化曲线中M=M_S/3磁化平台,得到平台宽度随不同的自旋交换相互作用强弱的变化关系,以及出现磁化平台时格点的自旋构型;给出亚稳态存在的条件及亚稳态时的微观构型.研究磁滞回线随温度的变化关系.结果表明,随着温度的升高,磁滞回线逐渐减小,最终消失.     

Spin-Fluctuation Transition in the Disordered Ising Model

JETP Letters - A model of an impurity system in semiconductors consisting of spins randomly distributed in space with a hydrogen-like distance dependence of the exchange energy in the Ising...     

Effect of Magnetic Field on the Thermodynamic and Magnetic Properties of the Antiferromagnetic Ising Model on a Body-Centered Cubic Lattice

Physics of the Solid State - The effect of an external magnetic field on the phase transitions and the thermodynamic and magnetic properties of the three-dimensional antiferromagnetic Ising model...     

On the Ising Model with Random Boundary Condition

The infinite-volume limit behavior of the 2d Ising model under possibly strong random boundary conditions is studied. The model exhibits chaotic size-dependence at low temperatures and we prove that the + and – phases are the only almost sure limit Gibbs measures, assuming that the limit is taken along a sparse enough sequence of squares. In particular, we provide an argument to show that in a sufficiently large volume a typical spin configuration under a typical boundary condition contains no interfaces. In order to exclude mixtures as possible limit points, a detailed multi-scale contour analysis is performed.     

Dynamics of the Random Ising Model with Long-Range Interaction

Critical dynamics of the random Ising model with long-range interaction decaying as r-(d σ) where d is the dimensionality) is studied by the theoretic renormalization-group approach. The system is released to an evolution within a model A dynamics. Asymptotic scaling laws are studied in a frame of the expansion in = 2σ - d. In dimensions d ＜ 2σ. the dynamic exponent z is calculated to the second order in at the random fixed point.``     

Critical Point of the Honeycomb Antiferromagnetic Ising Model in a Nonzero Magnetic Field: An Analytical Analysis

In this paper we determined the critical point of the antiferromagnetic Ising model in a nonzero magnetic field on the honeycomb lattice by an analytical method-the generalized cumulant expansion with the mean field hypothesis. By calculating the magnetization to the fourth order correction, we get encouraging results when compared with the known numerical results by finite size analysis.     

Magnetic Properties of an Antiferromagnetic Spin-1/2 XYZ Model in the Presence of Different Magnetic Fields: Finite-Size Effects of Inhomogeneity Property*

Magnetic and thermodynamic properties of the anisotropic XYZ spin-1/2 finite chain under both homogeneous and inhomogeneous magnetic fields are theoretically studied at low temperature. Using exact diagonalization method (ED), we study the magnetization, magnetic susceptibility, and specific heat of the model characterized in terms of the finite correlation length in the presence of three different magnetic fields including longitudinal, transverse, and transverse staggered magnetic fields. The magnetization, susceptibility, and the specific heat of the model are investigated under two conditions separately: (i) When the model is putted in the presence of homogeneous magnetic fields. (ii) When finite inhomogeneities are considered for all applied magnetic fields in the Hamiltonian. We show that for the finite-size XYZ chains at low temperature, the evident magnetization plateaus gradually convert to their counterpart quasi-plateaus when the transverse magnetic field increases. Moreover, the influence of the transverse and staggered transverse magnetic fields, and their corresponding inhomogeneities on the magnetization process, magnetic susceptibility, and specific heat are reported in detail. Our exact results illustrate that by altering the inhomogeneity parameters, magnetization plateaus gradually convert to their counterpart quasi-plateaus. The specific heat manifests Schottky-type maximum, double-peak, and triple-peak, as well as, transformation between them by varying considered inhomogeneity parameters in the Hamiltonian.     

The Duality Transformation for an n-Species Ising Model Interacting with Z2 Gauge Fields on a Random Surface

The duality transformation is carried out for an n-species Ising spin system interacting with Z₂ gauge fields. For n > 1, we find that the dual model has topological terms when the surface is topologically nontrivial. The plaquette interaction of the gauge fields is dual to an n-spin coupling in the dual model.     

Effects of Superaging and Percolation Crossover on the Nonequilibrium Critical Behavior of the Two-Dimensional Disordered Ising Model

A Monte Carlo study of the specific features of the nonequilibrium critical behavior has been performed for the two-dimensional “pure” and structurally disordered Ising models in the course of their evolution from the low-temperature initial state at spin concentrations p = 1.0, 0.9, and 0.8. It is shown for the first time that the pinning of domain walls by structural defects leads to the anomalously strong slowing down in the evolution of the autocorrelation function characterized by the superaging effect with exponents μ = 6.25(5) and μ = 6.75(5) for the model with the spin concentrations p = 0.9 and 0.8, respectively. The pure model exhibits the conventional aging with the exponent μ = 1. It is found that the superaging effects in structurally disordered systems lead to vanishing of the limiting fluctuation?dissipation ratio X^∞, whereas X^∞ = 0.751(24) for the pure model.     

Thermodynamic Transitions of Antiferromagnetic Ising Model on the Fractional Multi-branched Husimi Recursive Lattice

The multi-branched Husimi recursive lattice is extended to a virtual structure with fractional numbers of branches joined on one site. Although the lattice is undrawable in real space, the concept is consistent with regular Husimi lattice. The Ising spins of antiferromagnetic interaction on such a set of lattices are calculated to check the critical temperatures (T_c) and ideal glass transition temperatures (T_k) variation with fractional branch numbers. Besides the similar results of two solutions representing the stable state (crystal) and metastable state (supercooled liquid) and indicating the phase transition temperatures, the phase transitions show a well-defined shift with branch number variation. Therefore the fractional branch number as a parameter can be used as an adjusting tool in constructing a recursive lattice model to describe real systems.     

Weak Universality in the Disordered Two-Dimensional Antiferromagnetic Potts Model on a Triangular Lattice

The critical behavior of the disordered two-dimensional antiferromagnetic Potts model with the number of spin states q= 3 on a triangular lattice with disorder in the form of nonmagnetic impurities is studied by the Monte Carlo method. The critical exponents for the susceptibility γ, magnetization β, specific heat α, and correlation radius ν are calculated in the framework of the finite-size scaling theory at spin concentrations p = 0.90, 0.80, 0.70, and 0.65. It is found that the critical exponents increase with the degree of disorder, whereas the ratios and do not change, thus holding the scaling equality \(\frac{{2\beta }}{\nu } + \frac{\gamma }{\nu } = d\). Such behavior of the critical exponents is related to the weak universality of the critical behavior characteristic of disordered systems. All results are obtained using independent Monte Carlo algorithms, such as the Metropolis and Wolff algorithms.     

Magnetic and Thermal Behaviour of One-Dimensional Antiferromagnetic Spin-1 Ising Chain at Low Temperatures

We investigate magnetic and thermal behaviours of one-dimensional antiferromagnetic spin-i Ising chain with single-ion anisotropy at very low temperatures using the classical transfer matrix technique. Magnetic plateaus, phase diagram, specific heat, susceptibility of the spin chain have been evaluated numerically from the free energy. The results are in good agreement with the experimental data for the spin-1 compounds [Ni2 （Medpt）2 （μ- ox）（H2O）2]（ClO4）22H2O, [Ni2（Medpt）2（μ-ox）（μ-N3）]（ClO4）0.5H2O, Ni（C2H8N2）Ni（CN）4 and Ni（C10H8N2）2 Ni（CN）4·H2O.     

Non-degenerated Ground States and Low-degenerated Excited States in the Antiferromagnetic Ising Model on Triangulations

We study the unexpected asymptotic behavior of the degeneracy of the first few energy levels in the antiferromagnetic Ising model on triangulations of closed Riemann surfaces. There are strong mathematical and physical reasons to expect that the number of ground states (i.e., degeneracy) of the antiferromagnetic Ising model on the triangulations of a fixed closed Riemann surface is exponential in the number of vertices. In the set of plane triangulations, the degeneracy equals the number of perfect matchings of the geometric duals, and thus it is exponential by a recent result of Chudnovsky and Seymour. From the physics point of view, antiferromagnetic triangulations are geometrically frustrated systems, and in such systems exponential degeneracy is predicted. We present results that contradict these predictions. We prove that for each closed Riemann surface S of positive genus, there are sequences of triangulations of S with exactly one ground state. One possible explanation of this phenomenon is that exponential degeneracy would be found in the excited states with energy close to the ground state energy. However, as our second result, we show the existence of a sequence of triangulations ${(\mathcal{T}_n)}$ of a closed Riemann surface of genus 10 with exactly one ground state such that the degeneracy of each of the 1^st, 2^nd, 3^rd and 4^th excited energy levels belongs to O(n), O(n ²), O(n ³) and O(n ⁴), respectively.     

Generalized Ising Model in the Absence of Magnetic Field

Journal of Experimental and Theoretical Physics - The Ising model on an one-dimensional monoatomic equidistant lattice with different exchange interactions between atomic spins at the sites of...     

Generalized Ising Model in a Magnetic Field

Journal of Experimental and Theoretical Physics - Results on the generalization of the Ising model to an arbitrary number of translations of a linear chain in an external magnetic field, taking...     

The Lifshitz Tail and Relaxation to Equilibrium in the One-Dimensional Disordered Ising Model

We study spectral properties of the generator of the Glauber dynamics for a 1D disordered stochastic Ising model with random bounded couplings. By an explicit representation for the upper branch of the generator we get an asymptotic formula for the integrated density of states of the generator near the upper edge of the spectrum. This asymptotic behavior appears to have the form of the Lifshitz tail, which is typical for random operators near fluctuation boundaries. As a consequence we find the asymptotics for the average over the disorder of the time-autocorrelation function to be $$\langle \langle \sigma _{\text{0}}^\omega (t),\sigma _0 (0)\rangle _{P(\omega ) = } {\text{exp\{ }} - gt - kt^{1/3} {\text{(1 + }}o(1){\text{)\} as }}t \to \infty $$ with constants g, k depending on the distribution of the random couplings.