Lifshitz-point correlation length exponents from the large-n expansion

The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m  -axial Lifshitz points. We derive the leading non-trivial 1/n$1/n$ correction for the perpendicular correlation-length exponent _νL2${\nu }_{L2}$ and hence several related thermal exponents to order O(1/n)$O(1/n)$. The results are consistent with known large-n expansions for d  -dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d^?=4+m/2$d^{?}=4+m/2$ for generic m∈[0,d]$m\in [0,d]$. Analytical results are given for the special case d=4$d=4$, m=1$m=1$. For uniaxial Lifshitz points in three dimensions, 1/n$1/n$ coefficients are calculated numerically. The estimates of critical exponents at d=3$d=3$, m=1$m=1$ and n=3$n=3$ are discussed.     

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.     

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.     

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.     

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$p=1/4$.     

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.     

On DBI Textures with generalized Hopf fibration

In this Letter we show numerical existence of O(4)$O(4)$ Dirac–Born–Infeld (DBI) Textures living in (N+1)$(N+1)$ dimensional spacetime. These defects are characterized by S^N→S³$S^N\to S^3$ mapping, generalizing the well-known Hopf fibration into _πN(S³)${\pi }_N(S^3)$, for all N>3$N>3$. The nonlinear nature of DBI kinetic term provides stability against size perturbation and thus renders the defects having natural scale.     

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.     

What if supersymmetry breaking appears below the GUT scale?

We consider the possibility that the soft supersymmetry-breaking parameters m_1/2$m_{1/2}$ and m₀$m_0$ of the MSSM are universal at some scale Min$M_{\mathrm{in}}$ below the supersymmetric grand unification scale MGUT$M_{\mathrm{GUT}}$, as might occur in scenarios where either the primordial supersymmetry-breaking mechanism or its communication to the observable sector involve a dynamical scale below MGUT$M_{\mathrm{GUT}}$. We analyze the (m_1/2,m₀)$(m_{1/2},m_0)$ planes of such sub-GUT CMSSM models, noting the dependences of phenomenological, experimental and cosmological constraints on Min$M_{\mathrm{in}}$. In particular, we find that the coannihilation, focus-point and rapid-annihilation funnel regions of the GUT-scale CMSSM approach and merge when Min∼¹⁰¹² GeV$M_{\mathrm{in}}\sim {10}^{12}\text{GeV}$. We discuss sparticle spectra and the possible sensitivity of LHC measurements to the value of Min$M_{\mathrm{in}}$.     

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$\mathrm{\Delta }{G}_2=0.0035{\text{ GeV}}^4$.     

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$\gamma =1.75$.     

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$g_c$.     

Dynamical properties of a dissipative discontinuous map: A scaling investigation

The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action 〈I²〉$〈I^2〉$ as a function of the n-th iteration of the map as well as the parameters K and γ  , controlling nonlinearity and dissipation, respectively. We concentrate our efforts to study the case where the nonlinearity is large; i.e., K?1$K?1$. In this regime and for large initial action _I0?K$I_0?K$, we prove that dissipation produces an exponential decay for the average action 〈I〉$〈I〉$. Also, for _I0≅0$I_0\cong 0$, we describe the behavior of 〈I²〉$〈I^2〉$ using a scaling function and analytically obtain critical exponents which are used to overlap different curves of 〈I²〉$〈I^2〉$ onto a universal plot. We complete our study with the analysis of the scaling properties of the deviation around the average action ω.     

Long-range memory elementary 1D cellular automata: Dynamics and nonextensivity

We numerically study the dynamics of elementary 1D cellular automata (CA), where the binary state _σi(t)∈{0,1}${\sigma }_i(t)\in \{0,1\}$ of a cell i   does not only depend on the states in its local neighborhood at time t-1$t-1$, but also on the memory of its own past states _σi(t-2),_σi(t-3),…,_σi(t-τ),…${\sigma }_i(t-2),{\sigma }_i(t-3),\dots ,{\sigma }_i(t-\tau ),\dots$ . We assume that the weight of this memory decays proportionally to τ^-α${\tau }^{-\alpha }$, with α?0$\alpha ?0$ (the limit α→∞$\alpha \to \infty$ corresponds to the usual CA). Since the memory function is summable for α>1$\alpha >1$ and nonsummable for 0?α?1$0?\alpha ?1$, we expect pronounced changes of the dynamical behavior near α=1$\alpha =1$. This is precisely what our simulations exhibit, particularly for the time evolution of the Hamming distance H   of initially close trajectories. We typically expect the asymptotic behavior H(t)∝t^1/(1-q)$H(t)\propto t^{1/(1-q)}$, where q   is the entropic index associated with nonextensive statistical mechanics. In all cases, the function q(α)$q(\alpha )$ exhibits a sensible change at α?1$\alpha ?1$. We focus on the class II rules 61, 99 and 111. For rule 61, q=0$q=0$ for 0?α?_αc?1.3$0?\alpha ?{\alpha }_c?1.3$, and q<0$q<0$ for α>_αc$\alpha >{\alpha }_c$, whereas the opposite behavior is found for rule 111. For rule 99, the effect of the long-range memory on the spread of damage is quite dramatic. These facts point at a rich dynamics intimately linked to the interplay of local lookup rules and the range of the memory. Finite size scaling studies varying system size N   indicate that the range of the power-law regime for H(t)$H(t)$ typically diverges ∝N^z$\propto N^z$ with 0?z?1$0?z?1$.     

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.