Electronic properties of a Penrose tiling lattice in a magnetic field

The one-electron energy spectrum of a two-dimensional Penrose tiling lattice in a uniform magnetic field is calculated as a function of magnetic fields with a tight-binding Hamiltonian. The calculated results show the following remarkable features characteristic of the Penrose lattice. (1) The density of states in a magnetic field has a central peak with zero width at the zero energy. It is shown that the zero-energy states correspond to the ring states in which the wavefunction has a non-vanishing amplitudes only at the sites on a ring-like region around the origin. (2) The energy levels coalesce into Landau type levels and the boundary states due to the finite size effects based on a fixed boundary condition appear in the gap region between Landau levels. (3) The magnetic field dependence of the energy spectrum has a repeated pattern of self-similarity with the golden mean ratio of two successive periods.     

Dynamic magnetic behavior of the mixed spin （2, 5/2） Ising system with antiferromagnetic/antiferromagnetic interactions on a bilayer square lattice

Using the mean-field theory and Glauber-type stochastic dynamics, we study the dynamic magnetic properties of the mixed spin （2, 5/2） Ising system for the antiferromagnetic/antiferromagnetic （AFM/AFM） interactions on the bilayer square lattice under a time varying （sinusoidal） magnetic field. The time dependence of average magnetizations and the thermal variation of the dynamic magnetizations are examined to calculate the dynamic phase diagrams. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and the effects of interlayer coupling interaction on the critical behavior of the system are investigated. We also investigate the influence of the frequency and find that the system displays richer dynamic critical behavior for higher values of frequency than that of the lower values of it. We perform a comparison with the ferromagnetic/ferromagnetic （FM/FM） and AFM/FM interactions in order to see the effects of AFM/AFM interaction and observe that the system displays richer and more interesting dynamic critical behaviors for the AFM/AFM interaction than those for the FM/FM and AFM/FM interactions.     

Behavior of Ising spin glasses in a magnetic field

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field-temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.     

Condensate oscillations in a Penrose tiling lattice

We study the dynamics of a Bose-Einstein condensate subject to a particular Penrose tiling lattice. In such a lattice, the potential energy at each site depends on the neighbour sites, accordingly to the model introduced by Sutherland [16]. The Bose-Einstein wavepacket, initially at rest at the lattice symmetry center, is released. We observe a very complex time-evolution that strongly depends on the symmetry center (two choices are possible), on the potential energy landscape dispersion, and on the interaction strength. The condensate-width oscillates at different frequencies and we can identify large-frequency reshaping oscillations and low-frequency rescaling oscillations. We discuss in which conditions these oscillations are spatially bounded, denoting a self-trapping dynamics.     

Two-spin correlation function of spin 12 Ising model on a bethe lattice

The two-spin correlation function of the Ising model on a Bethe lattice as a function of temperature and magnetic field. It is found that the coherence length is finite at finite temperatures.     

Square lattice Ising antiferromagnet in an external magnetic field

We study the anisotropic square lattice Ising antiferromagnet in terms of three parameters: an external magnetic field B, an effective temperature and an anisotropy parameterK. The model, i.e., partition function and free energy, is solved exactly in the anisotropic limit,K0, for arbitrary temperature and field by using the transfer matrix method. We also calculate the first corrections beyond this limit. The limit is non trivial and the phase transition is completely preserved. It is of the expected Ising type. The transition temperature _c (B, K) is determined exactly for bothK0 andK and the results are used to check the validity of a recently conjectured formula by Müller-Hartmann and the author.     

Low energy spin waves and magnetic interactions in SrFe2As2

We report inelastic neutron scattering studies of magnetic excitations in antiferromagnetically ordered SrFe2As2 (T_{N}=200-220 K), the parent compound of the FeAs-based superconductors. At low temperatures (T=7 K), the magnetic spectrum S(Q,Planck's omega) consists of a Bragg peak at the elastic position (Planck's omega=0 meV), a spin gap (Delta< or =6.5 meV), and sharp spin-wave excitations at higher energies. Based on the observed dispersion relation, we estimate the effective magnetic exchange coupling using a Heisenberg model. On warming across T_{N}, the low-temperature spin gap rapidly closes, with weak critical scattering and spin-spin correlations in the paramagnetic state. The antiferromagnetic order in SrFe2As2 is therefore consistent with a first order phase transition, similar to the structural lattice distortion.     

The magnetic susceptibility of two-dimensional Ising model on a finite-size lattice

The form factor representation of the correlation function of the 2D Ising model on a cylinder is generalized to the case of arbitrary arrangement of correlating spins. The magnetic susceptibility on a lattice, one of whose dimensions (N) is finite, is calculated in both the ferromagnetic and the paramagnetic region of the parameters of the model. The structure of singularities of susceptibility in the complex temperature plane at finite values of N and the transition to the thermodynamic limit N→∞ are discussed.     

Re-entrant ferromagnetism in a two-dimensional mixed spin Ising model with random nearest-neighbour interactions

Using the finite cluster approximation we study a mixed spin model with random interactions on a ferrimagnetic square lattice (with spins =1/2 andS=1). The interactions are assumed to be independent random variables with distribution,P(K _ij )=p(K _ij –K)+(1–p) (K _ij –K), whereK>0 and ||1. In a certain range of negative values of the phase diagrams exhibit re-entrant behaviour. This indicates that re-entrance seems to be a characteristic feature of systems in which both frustration and disorder are present.On leave from Faculté des Sciences I, Université Hassan II, Casablanca, Morocco; and Laboratoire de Magnétisme Université de Rabat, MoroccoSupported by the agreement of cooperation between the DFG and the CNR-Maroc.     

Continuum limit on a 2-dimensional random lattice

We investigate the continuum limit of the Ising model on a 2-dimensional random lattice using Monte Carlo and strong coupling techniques. No evidence is found for deviation from the behaviour of the standard Ising model on a regular lattice; we do not see the modified critical properties found in the bond-diluted Ising model. Our results suggest that the continuum limit is the usual non-interacting Majorana fermion theory.     

Yangian symmetry and Virasoro character in a lattice spin system with long-range interactions

We consider the symmetry of lattice su(n) spin systems with inverse square exchange; the Haldane-Shastry model and the Polychronakos-Frahm model. It is shown that both systems have yangian symmetry for a finite number of sites. Based on the yangian symmetry the energy spectrum is considered. Furthermore the representation for motifs and the relations with the Virasoro character for su(n) level-1 Wess-Zumino- Witten theory are discussed.     

Spin-1/2 Ising model on a AFM/FM two-layer Bethe lattice in a staggered magnetic field

A bilayer spin-1/2 Ising model consisting of two superposed Bethe lattices with antiferromagnetic/ferromagnetic interactions is studied by the use of exact recursion relations in a pairwise approach in the presence of an external staggered magnetic field. Besides the ground state phase diagrams calculated in different possible planes of the model parameters space, the thermal variations of the order-parameters and the free energy are investigated to obtain the temperature-dependent phase diagrams of the model for different values of the coordination numbers q. Our calculations reveal that depending on the strength of the model parameters, the model exhibits a variety of interesting phase transitions and therefore phase diagrams.     

Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field

We consider a one-dimensional Ising model in a transverse magnetic field coupled to a dissipative heat bath. The phase diagram and the critical exponents are determined from extensive Monte Carlo simulations. It is shown that the character of the quantum phase transition is radically altered from the corresponding nondissipative model and the double well coupled to a dissipative heat bath with linear friction. Spatial couplings and the dissipative dynamics combine to form a new quantum criticality which is independent of dissipation strength.     

二维正方晶格Compass-Ising模型的方向序和磁有序

采用Monte Carlo方法研究二维正方晶格Compass-Ising模型的低温性质.通过调节过渡参量 ,计算了阻挫对方向序和磁有序的影响. 结果表明,阻挫的增加,易于形成方向序,同时会抑制磁有序. 当阻挫足够强时,磁有序将被破坏. 方向序和磁有序间的转变是一个逐渐过渡的过程,并不存在明显相变.     

Critical phenomena for a triangular spin lattice I: Triplet interactions

Critical phenomena in an Ising-like spin system on a triangular lattice are studied by means of the renormalization theory. The critical indices of the critical point due to triplet interactions are determined approximately, in fair agreement with the exponents, known from the exact solution due to Baxter and Wu. The cross-over from triplet critical behavior to ferromagnetic (nearest neighbor) critical behavior is calculated.