Zeros of the Potts model partition function on Sierpinski graphs

We calculate zeros of the q-state Potts model partition function on m  ?th-iterate Sierpinski graphs, _Sm$S_m$, in the variable q and in a temperature-like variable, y  . We infer some conjectured asymptotic properties of the loci of zeros in the limit m→∞$m\to \infty$ and relate these to thermodynamic properties of the q  -state Potts ferromagnet and antiferromagnet on the Sierpinski gasket fractal, _S∞$S_{\infty }$.     

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=∞$E=\infty$.     

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.     

Percolation theory and fragmentation measures in social networks

We study the statistical properties of a recently proposed social networks measure of fragmentation F after removal of a fraction q of nodes or links from the network. The measure F   is defined as the ratio of the number of pairs of nodes that are not connected in the fragmented network to the total number of pairs in the original fully connected network. We compare this measure with the one traditionally used in percolation theory, _P∞$P_{\infty }$, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods, we study Erd?s–Rényi (ER) and scale-free (SF) networks under various node removal strategies. We find that for a network obtained after removal of a fraction q   of nodes above criticality, _P∞≈(1-F)^1/2$P_{\infty }\approx (1-F{)}^{1/2}$. For fixed _P∞$P_{\infty }$ and close to criticality, we show that 1-F$1-F$ better reflects the actual fragmentation. For a given _P∞$P_{\infty }$, 1-F$1-F$ has a broad distribution and thus one can improve significantly the fragmentation of the network. We also study and compare the fragmentation measure F   and the percolation measure _P∞$P_{\infty }$ for a real national social network of workplaces linked by the households of the employees and find similar results.     

The extended Higgs system in R-symmetric supersymmetry theories

The Higgs sector is extended in R  -symmetric supersymmetry theories by two iso-doublets R_d,u$R_{d,u}$ which complement the standard iso-doublets H_d,u$H_{d,u}$. We have analyzed masses and interactions of these novel states and describe their [non-standard] decay modes and their production channels at the LHC and e⁺e⁻$e^{+}{e}^{-}$ colliders.     

Fluxmetric and magnetometric demagnetizing factors for cylinders

Fluxmetric and magnetometric demagnetizing factors, _Nf$N_{\mathrm{f}}$ and _Nm$N_{\mathrm{m}}$, for cylinders along the axial direction are numerically calculated as functions of material susceptibility χ$\chi$ and the ratio γ$\gamma$ of length to diameter. The results have an accuracy better than 0.1% with respect to min(_Nf,m,1-_Nf,m)$\min (N_{\mathrm{f},\mathrm{m}},1-N_{\mathrm{f},\mathrm{m}})$ and are tabulated in the range of 0.01?γ?500$0.01?\gamma ?500$ and -1?χ<∞$-1?\chi <\infty$. _Nm$N_{\mathrm{m}}$ along the radial direction is evaluated with a lower accuracy from _Nm$N_{\mathrm{m}}$ along the axis and tabulated in the range of 0.01?γ?1$0.01?\gamma ?1$ and -1?χ<∞$-1?\chi <\infty$. Some previous results are discussed and several applications are explained based on the new results.     

Superconductivity in Ba2/3Pt3B2 with the Kagome lattice

Resistivity, magnetization and low temperature specific heat (down to 0.4 K) of Ba_2/3Pt₃B₂ with the Kagome lattice of the transition metal Pt atoms have been investigated. The magnetization hysteresis loops measured on the sample indicate that it belongs to a type-II superconductor. The specific heat exhibits ΔC/γ_nT|_Tc≈1.7$\Delta C/{\gamma }_{n}T{|}_{T_c}\approx 1.7$, showing a moderate coupling superconductivity. Furthermore, the magnetic field dependence of the electronic specific heat coefficient in the low temperature limit demonstrates a linear relation γ_e∝H${\gamma }_e\propto H$, suggesting an s-wave gap. Surprisingly, the Wilson ratio determined here is about 34, which may be explained by short range magnetic correlation. Compared with the compound LaRu₃Si₂, we intend to attribute the extraordinarily large Wilson ratio to the deficiency of Ba atoms. Further theoretical and experimental efforts are required to clarify this issue.     

Thermodynamics properties of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H$H$ and transverse magnetic field Ω$\Omega$. Using the effective-field theory (EFT) with correlation in cluster with N=1$N=1$ spin we calculate the thermodynamic properties as a function of temperature with values H$H$ and Ω$\Omega$ fixed. The model consists of ferromagnetic interaction _Jx$J_x$ in the x$x$ direction and antiferromagnetic interaction _Jy$J_y$ in the y$y$ direction, and it is found that for H/_Jy∈[0,2]$H/J_y\in [0,2]$ the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=_Jx/_Jy=1$\lambda =J_x/J_y=1$ (isotropic square lattice).     

The Haldane–Shastry spin chain and the topological basis realization

In this paper, based on the topological basis states, we investigate the Hamiltonian family {H₂,H₃,H₄}$\{H_2,H_3,H_4\}$ of a closed four-qubit Haldane–Shastry spin chain. Not only the two-qubit interaction form, but also the three-qubit interaction form and the four-qubit interaction form are presented in terms of spin operators. Meanwhile, we explore some particular properties of the topological basis states in these systems. With Yangian algebra, the symmetry of the systems and the transitions between the eigenstates have been investigated. We find a really useful effect of Y(sl(2))$Y\left(sl\left(2\right)\right)$ operators {J_±,J₃}$\{J_{\pm },J_3\}$, which is that they can describe the transitions between the spin single state and the spin triple states. Furthermore, we construct a new Hamiltonian, whose energy degeneracies can be changed by adjusting the strengths of the two-qubit interactions, three-qubit interactions, four-qubit interactions, and the external magnetic field.     

Terahertz spectroscopy of multiferroic EuFe3(BO3)4

The terahertz spectra of a rare-earth iron borate with the huntite structure are obtained for the first time. We study the low-temperature (4.0–90 K) α-polarized transmittance spectra of the EuFe₃(BO₃)₄ single crystal in the region 0.9–6.0 THz. Pronounced shifts of phonon frequencies and appearance of new phonon modes at the temperature _TS=58 K$T_S=58\text{K}$ of the R32→P₃₁21$R32\to P{3}_{1}21$ structural phase transition are observed. Additional shifts of phonon frequencies occur at the temperature _TN=34 K$T_N=34\text{K}$ of the magnetic ordering of the Fe subsystem, thus evidencing the spin–phonon coupling in this multiferroic material.     

Effect of Co layer thickness on the magnetic properties of Tb30Co70/SiNx/Co thin films

The SiN_x (20 nm)/Tb₃₀Co₇₀ (90 nm)/SiN_x (5 nm)/Co (3–37 nm)/SiN_x (10 nm)/Si multilayer films are deposited on naturally oxidized Si wafer by magnetron sputtering. The saturation magnetization (M_s) of the multilayer films is increased with the thickness of high M_s ferromagnetic Co layer. The perpendicular coercivity (_Hc⊥$H_{{\mathrm{c}}^{\perp }}$) value is increased with Co layer thickness as the thickness of the Co layer is lower than 15 nm and then decreases drastically when the thickness of the Co layer further increased. The increase of the _Hc⊥$H_{{\mathrm{c}}^{\perp }}$ value is owing to the interlayer exchange effect [Li Zhang, Physica B 390 (2007) 373] between TbCo and Co layers. Co under-layer with in-plane magnetic anisotropy would pin the magnetic moment of the TbCo layer near by the Co layer and cause the value of _Hc⊥$H_{{\mathrm{c}}^{\perp }}$ to increase. However, as the Co layer is thicker than a critical thickness, the _Hc⊥$H_{{\mathrm{c}}^{\perp }}$ value of the multilayer film would decrease. Therefore, the Co layer with in-plane magnetic anisotropy and soft magnetic properties is expected to dominate the magnetic properties of the multilayer films.     

Systematic study on QCD interactions of heavy mesons with ρ meson

The strong interactions of the negative-parity heavy mesons with ρ   meson may be described consistently in the context of an effective Lagrangian, which is invariant under isospin SU(2)$\mathit{SU}(2)$ transformation. Four coupling constants g_HHρ$g_{HH\rho }$, f_H∗Hρ$f_{H^{\ast }H\rho }$, g_H∗H∗ρ$g_{H^{\ast }{H}^{\ast }\rho }$ and f_H∗H∗ρ$f_{H^{\ast }{H}^{\ast }\rho }$ enter the effective Lagrangian, where H  (H^∗)$(H^{\ast })$ denotes a pseudoscalar bottom or charm meson (the corresponding vector meson). Using QCD light cone sum rule (LCSR) method and, as inputs, the hadronic parameters updated recently, we give an estimate of g_H∗H∗ρ$g_{H^{\ast }{H}^{\ast }\rho }$ and f_H∗H∗ρ$f_{H^{\ast }{H}^{\ast }\rho }$, about which little was known before, and present an improved result for g_HHρ$g_{HH\rho }$ and f_H∗Hρ$f_{H^{\ast }H\rho }$. Also, we examine the heavy quark asymptotic behavior of these nonperturbative quantities and assess the two low energy parameters β and λ of the corresponding effective chiral Lagrangian.     

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$g_c$.     

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.     

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.