A maximum entropy mean field method for driven diffusive systems

We introduce a method of generating systematic mean field (MF) approximations for the nonequilibrium steady state of ferromagnetic Ising driven diffusive systems (DDS), based on the maximum entropy principle due to Jaynes. In the phase coexistence region, MF approximations to the master equation do not provide a closed system of equations in the MF variables. This can be traced to the conservation of the order parameter by the stochastic dynamics. Our maximum entropy mean field (MEMF) approximation method is applicable to high temperatures as well to the low-temperature phase coexistence region. It is based on a derivation of a generalized variational free energy from the maximum entropy principle, with the MF evolution equations playing the role of constraints. In the phase coexistence region this free energy is nonconvex and is interpreted by means of a Maxwell construction. We use a pair-level variant of the MEMF approximation to calculate quantities of interest for the ferro-magnetic Ising DDS on a square lattice. Results of calculations with several different choices of transition rates satisfying local detailed balance are discussed and compared with those obtained by other methods.     

Auxiliary Vertices Method for Kagomé-Lattice Eight-Vertex Model

We investigate a class of eight-vertex models on a Kagomé lattice. With the help of auxiliary vertices, the Kagomé-lattice eight-vertex model (KEVM) is related to an inhomogeneous system which leads to a one-parameter family of commuting transfer matrices. Using an equation for commuting transfer matrices, we determine their eigenvalues. From calculated eigenvalues the correlation length of the KEVM is derived with its full anisotropy. There are two cases: In the first case the anisotropic correlation length (ACL) is the same as that of the triangular/honeycomb-lattice Ising model. By the use of an algebraic curve, it is shown that the Kagomé-lattice Ising model, the diced-lattice Ising model, and the hard-hexagon model also have (essentially) the same ACL as the KEVM. In the second case we find that the ACL displays 12fold rotational symmetry.     

Layered Ising models on triangular and honeycomb lattices

We study inhomogeneous Ising models on triangular and honeycomb lattices. The nearest neighbour couplings can have arbitrary strength and sign such that the coupling distribution is translationally invariant in the direction of one lattice axis, i.e. the models have a layered structure. By using a transfer matrix method we derive closed form expressions for the partition functions and free energies. The critical temperatures are calculated. Phase transitions at a finite critical temperature are universally of Ising type. Models with no phase transition may show different behaviour atT=0, which is explicitly shown for fully frustrated models on square, triangular and honeycomb lattices. Finally, generalizations to layered Ising models on more general lattices are discussed.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Order-from-disorder effect in the exactly solved mixed spin-(1/2, 1) Ising model on fully frustrated triangles-in-triangles lattices

The mixed spin-(1/2, 1) Ising model on two fully frustrated triangles-in-triangles lattices is exactly solved with the help of the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the equivalent spin- 1/2 Ising model on a triangular lattice. It is shown that the mutual interplay between the spin frustration and single-ion anisotropy gives rise to various spontaneously ordered and disordered ground states, which differ mainly in an occurrence probability of the non-magnetic spin state of the integer-valued decorating spins. We have convincingly evidenced a possible coexistence of the spontaneous long-range order with a partial disorder within the striking ordered–disordered ground state, which manifests itself through a non-trivial criticality at finite temperatures as well. A rather rich critical behavior including the order-from-disorder effect and reentrant phase transitions with either two or three successive critical points is also found.     

Comparison of diluted antiferromagnetic Ising models on frustrated lattices in a magnetic field

We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antiferromagnetic Ising model on the three-dimensional pyrochlore lattice in a magnetic field pointing in the [111] direction, sometimes referred to as the “kagome-ice” problem. We discuss the similarity and dissimilarity of the magnetization curves of the “kagome-ice” state and the two-dimensional kagome lattice.     

Two-dimensional periodic frustrated ising models in a transverse field

We investigate the interplay of classical degeneracy and quantum dynamics in a range of periodic frustrated transverse field Ising systems at zero temperature. We find that such dynamics can lead to unusual ordered phases and phase transitions or to a quantum spin liquid (cooperative paramagnetic) phase as in the triangular and kagome lattice antiferromagnets, respectively. For the latter, we further predict passage to a bond-ordered phase followed by a critical phase as the field is tilted. These systems also provide exact realizations of quantum dimer models introduced in studies of high temperature superconductivity.     

Topological defects and magnetization processes for the triangular lattice of ising particles with an antiferromagnetic interaction

For the frustrated triangular lattice of Ising magnetic moments with an antiferromagnetic interaction, which is in a state with two sublattices, a new type of topological defects with zero energy in the approximation of the interaction between only the nearest-neighbors has been found. These defects have a nonzero magnetic moment, and the magnetization in a low field occurs via the formation of a system of such defects. These properties are valid for a 2D superstructure in the form of a triangular lattice of single-domain magnetic particles with perpendicular anisotropy and dipole coupling.     

Vortices in quantum spin systems

We examine spin vortices in ferromagnetic quantum Heisenberg models with planar anisotropy on two-dimensional lattices. The symmetry properties and the time evolution of vortices built up from spin-coherent states are studied in detail. Although these states show a dispersion typical for wave packets, important features of classical vortices are conserved. Moreover, the results on symmetry properties provide a construction scheme for vortex-like excitations from exact eigenstates, which have a well-controlled time evolution. Our approach works for arbitrary spin length both on triangular and square lattices. Received 2 October 1998     

Nonequilibrium relaxation and critical aging for driven Ising lattice gases

We employ Monte?Carlo simulations to study the nonequilibrium relaxation of driven Ising lattice gases in two dimensions. Whereas the temporal scaling of the density autocorrelation function in the nonequilibrium steady state does not allow a precise measurement of the critical exponents, these can be accurately determined from the aging scaling of the two-time autocorrelations and the order parameter evolution following a quench to the critical point. We obtain excellent agreement with renormalization group predictions based on the standard Langevin representation of driven Ising lattice gases.     

Quantum Coherence and Correlation in Spin Models with Dzyaloshinskii-Moriya Interaction

We study quantum coherence and quantum correlation for detecting quantum phase transition (QPT) by means of quantum renormalization group (QRG) in various spin chain models with Dzyaloshinskii-Moriya (DM) interaction, including XXZ model with DM interaction, Ising model with DM interaction and XY model with DM interaction. It is found that through enough QRG iterations, l ₁ norm quantum coherence and one-norm geometric quantum discord can effectively characterize QPT. We also discuss the effect of DM interaction and anisotropy on quantum coherence and quantum correlation.     

Conditions for quantum violation of macroscopic realism

Why do we not experience a violation of macroscopic realism in everyday life. Normally, no violation can be seen either because of decoherence or the restriction of coarse-grained measurements, transforming the time evolution of any quantum state into a classical time evolution of a statistical mixture. We find the sufficient condition for these classical evolutions for spin systems under coarse-grained measurements. However, there exist "nonclassical" Hamiltonians whose time evolution cannot be understood classically, although at every instant of time the quantum state appears as a classical mixture. We suggest that such Hamiltonians are unlikely to be realized in nature because of their high computational complexity.     

Efficient algorithm for random-bond ising models in 2D

We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm computes the partition function and correlation functions at a single temperature on any planar network of N Ising spins in O(N;{3/2}) time or less. The method can handle continuous or discrete bond disorder and is especially efficient in the case of bond or site dilution, where it executes in O(NlnN) time near the percolation threshold. We demonstrate its feasibility on the ferromagnetic Ising model and the +/-J random-bond Ising model and discuss the regime of applicability in cases of full frustration such as the Ising antiferromagnet on a triangular lattice.     

Critical behavior in a model of correlated percolation

We study the critical behavior of certain two-parameter families of correlated percolation models related to the Ising model on the triangular and square lattices, respectively. These percolation models can be considered as interpolating between the percolation model given by the + and – clusters and the Fortuin-Kasteleyn correlated percolation model associated to the Ising model. We find numerically on both lattices a two-dimensional critical region in which the expected cluster size diverges, yet there is no percolation.     

THE CRITICAL DYNAMICS OF THE KINETIC ISING MODELS ON THE SYSTEMS WITH Rmin> 2

We perform the exact TDRG transformations on the kinetic Ising model of the braced ladder whose R_min is 5. Within our knowledge, this is the only example that the exact TDRG transformations have been performed on a system with R_min >2. We show that under Achiam's linear response theory there must be important excitations of the multi-spin operators in the kinetic Ising models of the systems with R_min > 2, the dynamic critical behaviours of the systems are greatly affected by these excitations. Moreover, we get the conclusion that for the kinetic Ising models of the systems with R_min=∞ exact TDRG calculationa are impossible. The complete new and interesting results are given.     

High-temperature expansion for nonequilibrium steady states in driven lattice gases

We develop a controlled high-temperature expansion for nonequilibrium steady states of the driven lattice gas, the "Ising model" for nonequilibrium physics. We represent the steady state as P(eta) alpha e(-betaH(eta)-psi(eta)) and evaluate the lowest order contribution to the nonequilibrium effective interaction psi(eta). We see that, in dimensions d > or = 2, all models with nonsingular transition rates yield the same summable psi(eta), suggesting the possibility of describing the state as a Gibbs state similar to equilibrium. The models with the Metropolis rule show exceptional behavior.     

Ising model on self-avoiding walk chains

The phase transitions of nearest-neighbour interacting Ising models on self-avoiding walk (SAW) chains on square and triangular lattices have been studied using Monte Carlo technique. To estimate the transition temperature (T _c) bounds, the average number of nearest-neighbours (Z _eff) of spins on SAWs have been determined using the computer simulation results, and the percolation thresholds (p _c) for site dilution on SAWs have been determined using Monte Carlo methods. We find, for SAWs on square and triangular lattices respectively,Z _eff=2.330 and 3.005 (which compare very well with our previous theoretically estimated values) andp _c=0.022±0.003 and 0.045±0.005. When put in Bethe-Peierls approximations, the above values ofZ _eff givekT _c/J<1.06 and 1.65 for Ising models on SAWs on square and triangular lattices respectively, while, using the semi-empirical relation connecting the Ising modelT _c's andp _c's for the same lattices, we findkT _c/J0.57 and 0.78 for the respective models. Using the computer simulation results for the shortest connecting path lengths in SAWs on both kinds of lattices, and integrating the spin correlations on them, we find the susceptibility exponent =1.024±0.007, for the model on SAWs on two dimensional lattices.     

具有三角自旋环的伊辛-海森伯链的热纠缠

研究了具有三角自旋环的伊辛-海森伯链在磁场作用下的热纠缠性质.分别讨论了三角自旋环中自旋1/2粒子间相互作用的三种情形,即XXX,XXZ和XY Z海森伯模型.利用转移矩阵方法,数值计算了具有三角自旋环的伊辛-海森伯链的配对纠缠度.计算结果表明,外加磁场强度和温度对系统处于上述三种海森伯模型的热纠缠性质均有重要影响.给出了系统在不同的海森伯模型下,纠缠消失对应的临界温度随磁场强度的变化图,由此可以得到系统存在配对纠缠的参数区域,同时发现在特定的参数区域存在纠缠恢复现象.因此适当调节温度和磁场强度,可以有效调控具有三角自旋环的伊辛-海森伯链热纠缠性质.     

Zero-Temperature Dynamics of Ising Models on the Triangular Lattice

We consider the nature of spin flips of zero-temperature dynamics for ferromagnetic Ising models on the triangular lattice with nearest-neighbor interactions and an initial configuration chosen from a symmetric Bernoulli distribution. We prove that all spins flip infinitely many times for almost every realization of the dynamics and initial configuration.     

Random fields and the partially paramagnetic state of CsCo0.83Mg0.17Br3: critical scattering study

We have performed measurements of the critical neutron scattering on CsCo0.83Mg0.17Br3, a dilute stacked triangular lattice (STL) Ising antiferromagnet (AF). A two component line shape associated with the critical fluctuations appears at a temperature coincident with T(N1) observed in pure CsCoBr3. Such scattering is indicative of fluctuations in prototypical random field Ising model (RFIM) systems. The random field domain state arises in this case due to geometrical frustration within the STL Ising AF, which gives rise to a three sublattice Néel state, in which one sublattice is disordered. Magnetic vacancies nucleate AF domains in which the vacancies reside on the disordered sublattice thereby generating a RFIM state in the absence of an applied magnetic field.