Eight-vertex model of the quasicrystal

The eight-vertex Baxter model of interacting spins is equivalent to two interacting Ising models. The ice-type ferroelectric model is a particular case. In this paper the eight-vertex model is solved exactly for the Penrose nonperiodic tiling of the plane.     

Kagomé ice state in the dipolar spin ice Dy2Ti2O7

We have investigated the kagomé ice behavior of the dipolar spin-ice compound Dy2Ti2O7 in a magnetic field along a [111] direction using neutron scattering and Monte Carlo simulations. The spin correlations show that the kagomé ice behavior predicted for the nearest-neighbor interacting model, where the field induces dimensional reduction and spins are frustrated in each two-dimensional kagomé lattice, occurs in the dipole interacting system. The spins freeze at low temperatures within the macroscopically degenerate ground states of the nearest-neighbor model.     

Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model

We establish a relation between several entanglement properties in the Lipkin-Meshkov-Glick model, which is a system of mutually interacting spins embedded in a magnetic field. We provide analytical proofs that the single-copy entanglement and the global geometric entanglement of the ground state close to and at criticality behave as the entanglement entropy. These results are in deep contrast to what is found in one- dimensional spin systems where these three entanglement measures behave differently.     

Theory of matching rules for the 3-dimensional Penrose tilings

We consider packings of the two Ammann rhombohedra used for tiling the three dimensional space. We define decorations for the facets of the rhombohedra. Using elementary algebraic topology, we prove that any tiling by these rhombohedra with matching decorations is a quasiperiodic Penrose tiling. The proof does not involve any reference to self similarity.     

原子核代数模型中的F-旋混合态、回弯、电磁跃迁问题的研究

在原子核的代数模型框架下,讨论了集体回弯效应、较高自旋的Ｆ－旋混合对称态以及电磁跃迁几率等问题． The collective backbending effect, F spin mixed symmetry states have been studied for the nuclei with moderate high spins. It is found that there is an additional L(L+3) proportional term in the E2 transition rates in the sdg interacting boson model and solved the long standing problem of reduction of collectivity in the wave function of boson models. The electromagnetic transitions in the spdf interacting boson model have been calculated and compared with existing experimental...     

Generalized algebraic transformations and exactly solvable classical-quantum models

The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel interesting exact results for the hybrid classical-quantum models, which may for instance describe interacting many-particle systems composed of the classical Ising spins and quantum Heisenberg spins, the localized Ising spins and delocalized electrons, or many other hybrid systems of a mixed classical-quantum nature.     

Low-temperature phases of itinerant fermions interacting with classical phonons: The static Holstein model

We consider models of independent itinerant fermions interacting with classical continuous or discrete variables (spins), the static Holstein model being a special case. We prove for all values of the fermion-spin coupling and a special value of the fermion chemical potential and classical magnetic field, at which the average fermion density is one-half and the average total spin is zero, that there are two degenerate ground states of period two with antiferromagnetic order for the spins and fermions. The existence of two corresponding low-temperature phases is proven for large coupling and dimension two or more by using a Peierls argument. This generalizes results of Kennedy and Lieb for the Falicov-Kimball model.Dedicated to Philippe Choquard on the occasion of his 65th birthday.     

Full replica symmetry breaking in <Emphasis Type="Italic">p</Emphasis>-spin-glass-like systems

It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows describing the transition from the full replica symmetry breaking glass solution to stable first replica symmetry breaking glass solution in the case of non-reflective symmetry diagonal operators used instead of Ising spins. As an example, axial quadrupole moments in place of Ising spins are considered and the boundary value \({p_{{c_1}}} \cong 2.5\) is found.     

Collective relaxation of nuclear spins and “superradiance” of magnons in ferromagnets

The Heisenberg model of ferromagnet, which contains nuclear spins interacting with electronic spins of own atoms by means of hyperfine interaction, is considered. A nonlinear evolution equation for collective nuclear spin z-component is obtained for the initial condition with the inverted nuclear spins (of the value 1/2). The exact solution of this equation is obtained. The collective relaxation of nuclear spins reveals the cooperative behaviour of superradiant type accompanied by magnons generation.     

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, d≥1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.     

Generalized Quasi-Exactly-Solvable Quanta1 Problems,the Represent at ions and Differential Realization of General Deformation of su(2)

This paper is devoted to building the represen tation theory of the general deformation for su(2) and then using it to generalize the quasi-exactly-solvable quan tal (QESQ) problems. For the finite dimensional and infinite dimensional representations, two classes of generalized QESQ models are respectively constructed in terms of the differential realization of the general deformation of su(2). When the deformation is the q-deformation in the quantum group theory, the QESQ model is discussed in detail by associating it with the nonlinear precession of high spins in an external field.     

Order by thermal disorder in 2D planar rotator model with dipolar interactions

The energy of a square planar rotator model of spins interacting via dipolar forces is minimized by infinite inequivalent configurations corresponding to spins arranged on four interpenetrating sublattices making angles , , , with a reference axis, being arbitrary. This infinite degeneracy of the ground state is accidental in nature and one expects that it is removed by thermal fluctuations in agreement with Monte Carlo simulation. Indeed we find that the elementary excitation energies which depend on lead to a free energy which is a function of with minima at and corresponding to columnar configurations. This selection of columnar configurations out of the infinite ground state manifold is an example of order by thermal disorder. Received 4 August 1998     

On statistical thermodynamics of multicomponent systems II

The equivalent neighbour (EN) model of interacting continuous spherically symmetric spins with the length equal or smaller than unity is solved exactly for all values of the spin dimensionality, D. A surprising result is that only for D 628 the system undergoes phase transitions at temperatures lower than those of the EN model of interacting spins with the hypercubic symmetry. In the D → ∞ limit the equation of state in zero field is derived analytically and gives the Landau type behaviour in the whole range of temperatures.     

Pressure and variational principle for random Ising model

An Ising model traditionally is a model for a repartition of spins on a lattice. Griffiths and Lebowitz ([3. 5]) have considered distributions of spins which can occur only on some randomly prescribed sites—Edwards and Anderson have introduced models where the interaction was random ([6, 7]). In both cases, the formalism of statistical mechanics reduces mainly to a relativised variational principle, which has been proved recently by Walters and the author [1]. In this note, we show how that reduction works and formulate the corresponding results on an example of either model.     

A quantitative criteria for the coincidence problem

The cosmic coincidence problem is a serious challenge to dark energy model. We suggest a quantitative criteria for judging the severity of the coincidence problem. Applying this criteria to three different interacting models, including the interacting quintessence, interacting phantom, and interacting Chaplygin gas models, we find that the interacting Chaplygin gas model has a better chance to solve the coincidence problem. Quantitatively, we find that the coincidence index C for the interacting Chaplygin gas model is smaller than that for the interacting quintessence and phantom models by six orders of magnitude.     

Spin order in one-dimensional Kondo and Hund lattices

We study numerically the one-dimensional Kondo and Hund lattices consisting of localized spins interacting antiferromagnetically or ferromagnetically with the itinerant electrons, respectively. Using the density-matrix renormalization group we find, for both models and in the small coupling regime, the existence of new magnetic phases where the local spins order forming ferromagnetic islands coupled antiferromagnetically. Furthermore, by increasing the interaction parameter |J| we find that this order evolves toward the ferromagnetic regime through a spiral-like phase with longer characteristic wavelengths. These results shed new light on the zero temperature magnetic phase diagram for these models.     

Growing perfect decagonal quasicrystals by local rules

A local growth algorithm for a decagonal quasicrystal is presented. We show that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to form on the upper layer, successive 2D PPT layers can be added on top resulting in a perfect decagonal quasicrystalline structure in bulk with a point defect only on the bottom surface layer. Our growth rule shows that an ideal quasicrystal structure can be constructed by a local growth algorithm in 3D, contrary to the necessity of nonlocal information for a 2D PPT growth.     

Opinion Dynamics on Complex Networks with Communities

The Ising or Potts models of ferromagnetism have been widely used to describe locally interacting social or economic systems. We consider a related model, introduced by Sznajd to describe the evolution of consensus in the scale-free networks with the tunable strength （noted by Q） of community structure. In the Sznajd model, the opinion or state of any spins can only be changed by the influence of neighbouring pairs of similar connection spins. Such pairs can polarize their neighbours. Using asynchronous updating, it is found that the smaller the community strength Q, the larger the slope of the exponential relaxation time distribution. Then the effect of the initial upspin concentration p as a function of the final all up probability E is investigated by taking different initialization strategies, the random node-chosen initialization strategy has no difference under different community strengths, while the strategies of community node-chosen initialization and hub node-chosen initialization are different in fina/probability under different Q, and the latter one is more effective in reaching final state.     

Spectral moments for systems described by an ensemble of hamiltonians

We generalize Van Vleck's method of moments for disordered solid-state that can be described by an ensemble of hamiltonians. Special reference is made to N.M.R. spectroscopy. Inhomogeneous broadening for a sample of free spins and the more complex problem of interacting spins are discussed in detail. The cumulant expansion and the Liouville space formalism are introduced as tools to simplify the expressions for the moments and to obtain physical approximations. As a particular application the Sherrington-Kirkpatrick model for spin glasses is derived and interpreted physically.     

Griffiths inequalities for noninteractingN-vector (classical heisenberg) models and applications to interacting systems

An order relation for tensors is defined. With this ordering it is shown that in noninteractingN-vector models 〈σ_Aσ_B〉?〈σ_A〉〈σ_B〉 is positive. Applications to interacting models include a proof for the alignment of spins and the subadditivity of the free energy.