Comparative study between a two-dimensional anisotropic Heisenberg antiferromagnet with easy-axis single-ion anisotropy and one with easy-axis exchange anisotropy

Generally, in literature, easy-axis single ion anisotropy and easy-axis exchange anisotropy was treated in indistinct way. In this work we propose to perform a comparative study of the effects of these two easy-axis anisotropies on the behavior of the magnetization and the critical temperature (_Tc)$(T_{\mathrm{c}})$ in the 2D classical Heisenberg antiferromagnetic model. In order to study the low-temperature thermodynamics of this model, we should consider the contribution of anisotropic spin waves, using a self-consistent harmonic approximation (SCHA) theory. We compare the predictions of SCHA with numerical simulations on L×L$L\times L$ square lattices using Monte Carlo (MC) simulations, which include effects due to all thermodynamically allowed excitations. Our SCHA results are in good agreement with our MC simulations results and have shown that the strong K$K$ limit gives two different Ising-like behavior. In the exchange anisotropic case, the dependence of _Tc$T_{\mathrm{c}}$ on anisotropic parameter K$K$ becomes linear and in the single-ion anisotropic case, _Tc$T_{\mathrm{c}}$ becomes independent of K$K$. Also, using MC simulations and finite size scaling, we show that the critical exponents in the two anisotropic case are compatible with the 2D Ising values α=0.125$\alpha =0.125$ and γ=1.75$\gamma =1.75$.     

The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T$T$), frequency (w$w$), Onsager coefficient (γ$\gamma$) and external magnetic field (H$H$) near the second-order (_Tc)$\left(T_c\right)$ and first-order (_Tt)$\left(T_t\right)$ phase transition temperatures are examined for given coordination numbers q$q$ on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α)$\left(\alpha \right)$. Our investigations revealed that only one peak is obtained near _Tt$T_t$ and three peaks are found near _Tc$T_c$ when the Onsager coefficient is varied at a given constant frequency for q=3$q=3$. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4$q=3,4$ and 6 near _Tc$T_c$. The sound attenuation peaks are observed near _Tt$T_t$ at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.     

Damage spreading in a driven lattice gas model

We studied damage spreading in a Driven Lattice Gas (DLG) model as a function of the temperature T$T$, the magnitude of the external driving field E$E$, and the lattice size. The DLG model undergoes an order–disorder second-order phase transition at the critical temperature _Tc(E)$T_c\left(E\right)$, such that the ordered phase is characterized by high-density strips running along the direction of the applied field; while in the disordered phase one has a lattice-gas-like behavior. It is found that the damage always spreads for all the investigated temperatures and reaches a saturation value _Dsat$D_{sat}$ that depends only on T$T$. _Dsat$D_{sat}$ increases for T<_Tc(E=∞)$T<T_c(E=\infty )$, decreases for T>_Tc(E=∞)$T>T_c(E=\infty )$ and is free of finite-size effects. This behavior can be explained as due to the existence of interfaces between the high-density strips and the lattice-gas-like phase whose roughness depends on T$T$. Also, we investigated damage spreading for a range of finite fields as a function of T$T$, finding a behavior similar to that of the case with E=∞$E=\infty$.     

Three PT-symmetric Hamiltonians with completely different spectra

We discuss three Hamiltonians, each with a central-field part H₀$H_0$ and a PT-symmetric perturbation igz$igz$. When H₀$H_0$ is the isotropic Harmonic oscillator the spectrum is real for all g$g$ because H$H$ is isospectral to H₀+g²/2$H_0+g^2/2$. When H₀$H_0$ is the Hydrogen atom then infinitely many eigenvalues are complex for all g$g$. If the potential in H₀$H_0$ is linear in the radial variable r$r$ then the spectrum of H$H$ exhibits real eigenvalues for 0<g<g_c$0<g<g_c$ and a PT phase transition at g_c$g_c$.     

Transition between SU(4) and SU(2) Kondo effect

Motivated by experiments in nanoscopic systems, we study a generalized Anderson, which consist of two spin degenerate doublets hybridized to a singlet by the promotion of an electron to two conduction bands, as a function of the energy separation δ$\delta$ between both doublets. For δ=0$\delta =0$ or very large, the model is equivalent to a one-level SU(N$N$) Anderson model, with N=4$N=4$ and 2 respectively. We study the evolution of the spectral density for both doublets (ρ_1σ(ω)${\rho }_{1\sigma }(\omega )$ and ρ_2σ(ω)${\rho }_{2\sigma }(\omega )$) and their width in the Kondo limit as δ$\delta$ is varied, using the non-crossing approximation (NCA). As δ$\delta$ increases, the peak at the Fermi energy in the spectral density (Kondo peak) splits and the density of the doublet of higher energy ρ_2σ(ω)${\rho }_{2\sigma }(\omega )$ shifts above the Ferrmi energy. The Kondo temperature T_K (determined by the half-width at half maximum of the Kondo peak in density of the doublet of lower energy ρ_1σ(ω)${\rho }_{1\sigma }(\omega )$) decreases dramatically. The variation of T_K with δ$\delta$ is reproduced by a simple variational calculation.     

Is space-time symmetry a suitable generalization of parity-time symmetry?

We discuss space-time symmetric Hamiltonian operators of the form H=H₀+igH^′$H=H_0+ig{H}^{\prime }$, where H₀$H_0$ is Hermitian and g$g$ real. H₀$H_0$ is invariant under the unitary operations of a point group G$G$ while H^′$H^{\prime }$ is invariant under transformation by elements of a subgroup G^′$G^{\prime }$ of G$G$. If G$G$ exhibits irreducible representations of dimension greater than unity, then it is possible that H$H$ has complex eigenvalues for sufficiently small nonzero values of g$g$. In the particular case that H$H$ is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<g_c$0<g<g_c$, where g_c$g_c$ is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H$H$ may exhibit real or complex eigenvalues for g>0$g>0$. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.     

Semiempirical fine-tuning for Hartree–Fock ionization potentials of atomic ions with non-integral atomic number

Amovilli and March (2006) [8] used diffusion quantum Monte Carlo techniques to calculate the non-relativistic ionization potential I(Z)$I(Z)$ in He-like atomic ions for the range of (fractional) nuclear charges Z   lying between the known critical value _Zc=0.911$Z_{\mathrm{c}}=0.911$ at which I(Z)$I(Z)$ tends to zero and Z=2$Z=2$. They showed that it is possible to fit I(Z)$I(Z)$ to a simple quadratic expression. Following that idea, we present here a semiempirical fine-tuning of Hartree–Fock ionization potentials for the isoelectronic series of He, Be, Ne, Mg and Ar-like atomic ions that leads to excellent estimations of _Zc$Z_{\mathrm{c}}$ for these series. The empirical information involved is experimental ionization and electron affinity data. It is clearly demonstrated that Hartree–Fock theory provides an excellent starting point for determining I(Z)$I(Z)$ for these series.     

Coercive field of a polycrystalline ferrimagnet with uni-axial anisotropy

Unlike the coercive field _Hc$H_{\mathrm{c}}$ of a bulk ferrimagnet, which diverges at the compensation temperature _Tcomp$T_{\mathrm{comp}}$, the coercive field of a polycrystalline ferrimagnet with uni-axial anisotropy is shown to have a minimum at _Tcomp$T_{\mathrm{comp}}$. Despite this behavior, the field required for domain-wall motion still diverges at the compensation temperature. These ideas are used to treat a ferrimagnetic class of molecule-based magnets, the bimetallic oxalates, that exhibit a minimum coercivity at _Tcomp$T_{\mathrm{comp}}$.     

Strange attractor in the Potts spin glass on hierarchical lattices

The spin-glass q-state Potts model on d  -dimensional diamond hierarchical lattices is investigated by an exact real space renormalization group scheme. Above a critical dimension _dl(q)$d_l(q)$ for q>2$q>2$, the coupling constants probability distribution flows to a low-temperature strange attractor   or to the high-temperature paramagnetic fixed point, according to the temperature is below or above the critical temperature _Tc(q,d)$T_c(q,d)$. The strange attractor was investigated considering four initial different distributions for q=3$q=3$ and d=5$d=5$ presenting strong robustness in shape and temperature interval suggesting a condensed phase with algebraic decay.     

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T$T$, a quantum parameter g$g$, and the ratio p=−_J2/_J1$p=-J_2/J_1$, where _J1>0$J_1>0$ refers to ferromagnetic interactions between first-neighbour sites along the d$d$ directions of a hypercubic lattice, and _J2<0$J_2<0$ is associated with competing antiferromagnetic interactions between second neighbours along m≤d$m\le d$ directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0$g=0$ space, with a Lifshitz point at p=1/4$p=1/4$, for d>2$d>2$, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0$T=0$ phase diagram, there is a critical border, _gc=_gc(p)$g_c=g_c\left(p\right)$ for d≥2$d\ge 2$, with a singularity at the Lifshitz point if d<(m+4)/2$d<(m+4)/2$. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4$p=1/4$.     

Vacuum phase transition at nonzero baryon density

It is argued that the dominant contribution to the interaction of quark–gluon plasma at moderate T?Tc$T?T_c$ is given by the nonperturbative vacuum field correlators. Basing on that nonperturbative equation of state of quark–gluon plasma is computed and in the lowest approximation expressed in terms of absolute values of Polyakov lines for quarks and gluons Lfund(T),Ladj(T)=(Lfund)^9/4$L_{\mathrm{fund}}(T),L_{\mathrm{adj}}(T)={(L_{\mathrm{fund}})}^{9/4}$ known from lattice and analytic calculations. Phase transition at any μ   is described as a transition due to vanishing of one of correlators, DE(x)$D^E(x)$, which implies the change of gluonic condensate ΔG₂$\mathrm{\Delta }{G}_2$. Resulting transition temperature Tc(μ)$T_c(\mu )$ is calculated in terms of ΔG₂$\mathrm{\Delta }{G}_2$ and Lfund(Tc)$L_{\mathrm{fund}}(T_c)$. The phase curve Tc(μ)$T_c(\mu )$ is in a good agreement with lattice data. In particular Tc(0)=0.27$T_c(0)=0.27$; 0.19; 0.17 GeV$0.17\text{ GeV}$ for nf=0,2,3$n_f=0,2,3$ and fixed ΔG₂=0.0035 GeV⁴$\mathrm{\Delta }{G}_2=0.0035{\text{ GeV}}^4$.     

The anisotropic quantum spin-1/2 Heisenberg antiferromagnet in the presence of a longitudinal field on a bcc lattice

In this work we study the critical behavior of the quantum spin-1/2 anisotropic Heisenberg antiferromagnet in the presence of a longitudinal field on a body centered cubic (bcc) lattice as a function of temperature, anisotropy parameter (Δ)$(\Delta )$ and magnetic field (H  ), where Δ=0$\Delta =0$ and 1 correspond the isotropic Heisenberg and Ising models, respectively. We use the framework of the differential operator technique in the effective-field theory with finite cluster of N  =4 spins (EFT-4). The staggered _ms=(_mA−_mB)/2$m_s=(m_A-m_B)/2$ and total m=(_mA+_mB)/2$m=(m_A+m_B)/2$ magnetizations are numerically calculated, where in the limit of _ms→0$m_s\to 0$ the critical line _TN(H,Δ)$T_N(H,\Delta )$ is obtained. The phase diagram in the T−H$T-H$ plane is discussed as a function of the parameter Δ$\Delta$ for all values of H∈[0,_Hc(Δ)]$H\in [0,H_c(\Delta )]$, where _Hc(Δ)$H_c(\Delta )$ correspond the critical field (_TN=0)$(T_N=0)$. Special focus is given in the low temperature region, where a reentrant behavior is observed around of H=_Hc(Δ)≥_Hc(Δ=1)=8J$H=H_c(\Delta )\ge H_c(\Delta =1)=8J$ in the Ising limit, results in accordance with Monte Carlo simulation, and also was observed for all values of Δ∈[0,1]$\Delta \in [\mathrm{0,1}]$. This reentrant behavior increases with increase of the anisotropy parameter Δ$\Delta$. In the limit of low field, our results for the Heisenberg limit are compared with series expansion values.     

The role of dipolar interaction in nanocomposite permanent magnets

The effects of dipolar interactions on the magnetization behaviors and magnetic properties of the nanocomposite magnets have been studied by micromagnetic simulations. Numerical results show that the dipolar interaction plays an important role during the demagnetization process, especially in the magnets with large soft-phase content _vs$v_{\mathrm{s}}$. For the isotropic nanocomposites, the remanence enhancement can be controlled through adjustments of the grain size D   and _vs$v_{\mathrm{s}}$. However, the appearance of magnetic vortex state leads to a very low remanence in the magnets with large D   and _vs$v_{\mathrm{s}}$. The dependence of coercivity on D   and _vs$v_{\mathrm{s}}$ can be attributed to the exchange-induced magnetization reversal near the grain boundaries and the low nucleation field of soft phase, respectively. For the anisotropic nanocomposites, the reduced remanence _mr$m_{\mathrm{r}}$ is equal to 1.0$1.0$ for the magnets with small D   or with low _vs$v_{\mathrm{s}}$. However, _mr$m_{\mathrm{r}}$ decreases with increasing _vs$v_{\mathrm{s}}$ for the magnet with large D   due to the influence of dipolar interactions. The difference between the calculated coercivity _Hc$H_{\mathrm{c}}$ with and without considering dipolar interaction shows that the dipolar interaction plays a more important role during the magnetization reversal in the soft phase than that in the hard phase. The maximum calculated energy product of the isotropic nanocomposites is only about 40 MGOe due to the conflicting relation between remanence and coercivity, while that of the anisotropic nanocomposites is 112 MGOe. This reminds us that the alignment of hard grain is important to obtain high performance.     

Diffusion-limited aggregates grown on nonuniform substrates

In the present paper, patterns of diffusion-limited aggregation (DLA) grown on nonuniform substrates are investigated by means of Monte Carlo simulations. We consider a nonuniform substrate as the largest percolation cluster of dropped particles with different structures and forms that occupy more than a single site on the lattice. The aggregates are grown on such clusters, in the range the concentration, p$p$, from the percolation threshold, _pc$p_c$ up to the jamming coverage, _pj$p_j$. At the percolation threshold, the aggregates are asymmetrical and the branches are relatively few. However, for larger values of p$p$, the patterns change gradually to a pure DLA. Tiny qualitative differences in this behavior are observed for different k$k$ sizes. Correspondingly, the fractal dimension of the aggregates increases as p$p$ raises in the same range _pc≤p≤_pj$p_c\le p\le p_j$. This behavior is analyzed and discussed in the framework of the existing theoretical approaches.     

A modified Vicsek model for self-propelled agents with exponential neighbor weight and restricted visual field

Large flocks of wild beings can have coordinated motion with neither leading center nor global information. The Vicsek model and its new versions explained such collective behavior of self-propelled agents with the mechanism of un-weighted influence of neighbors and global visual field (GVF), which may not always fit the reality. In the present work, we take both exponential (λ$\lambda$) neighbor weight (ENW) and restricted visual field (RVF) into account, and investigate the combinatory effect of them. Based on this mechanism, in most cases of our simulation, stationary direction consensus _Va$V_a$ exhibits a maximum or decreases with VF$VF$, and a minimum convergence time _Tmin$T_{min}$ appears in RVF, which demonstrates that GVF is not necessary for coordinated motion, while RVF matched ENW would be reasonable. Moreover, we simulated various recipes for optimizing _Va$V_a$ and T$T$ in unfavorable cases, and found critical points separating inverse λ$\lambda$-dependent variations of T$T$. The present work may be useful in improving the efficiency of direction consensus of large flocks of artificial individuals besides the understanding of biological collective motion in nature.     

Domain wall propagation in Permalloy nanowires with a thickness gradient

The magnetization reversal behavior of Permalloy nanowires has been investigated using a magneto-optic Kerr effect setup. Nanowires with various widths, w=250$w=250$ nm to 3 μm and a thickness of t=10$t=10$ nm were fabricated by electron-beam lithography and subsequent lift-off. Furthermore, similar nanowires but with a thickness gradient along the nanowire axis have been prepared to investigate the influence of the gradient on the magnetic domain wall propagation. Magnetization hysteresis loops recorded on individual nanowires without a gradient are compared to corresponding wires with a thickness gradient. The dependence of the coercive field, _Hc$H_c$ vs. t/w$t/w$ shows a linear behavior for wires without a gradient. However, wires with a gradient display a more complex crossover behavior. We find a plateau in the _Hc$H_c$ vs. t/w$t/w$ curve at values of w$w$, where a transformation from transverse to vortex domain wall type is expected.     

Effect of La doping on magnetotransport and magnetic properties of double perovskite Sr2FeMoO6 system

We have investigated the magnetotransport and magnetic properties on polycrystalline samples of Sr_2−xLa_xFeMoO₆ (x=0$x=0$, 0.2, 0.4, 0.6, 0.8 and 1.0). The magnitude of intergrain tunneling magnetoresistance with low magnetic field of 0.88 T for x=0.2$x=0.2$ and 0.4$0.4$ samples are as large as 5% and 7% at room temperature and 13% and 10% at 10 K, respectively. The increase of coercivity (_Hc$H_{\mathrm{c}}$), ratio of remanent magnetization with respect to saturation magnetization (_Mr/_Ms$M_{\mathrm{r}}/M_{\mathrm{s}}$), high saturation fields, and reduction of the saturation magnetization indicate that random disorder of spin orientation is mainly responsible for enhancement of the low-field magnetoresistance for samples with x?0.4$x?0.4$. Whereas rapid drop of _Hc$H_{\mathrm{c}}$, _Mr/_Ms$M_{\mathrm{r}}/M_{\mathrm{s}}$, _Mr$M_{\mathrm{r}}$, and saturation fields for samples with x>0.4$x>0.4$ signifies the growth of antiphase boundary, which gives rise to lower values of low-field MR.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.