Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

Localization in the ground state of a disordered array of quantum rotators

We consider the zero-temperature behavior of a disordered array of quantum rotators given by the finite-volume Hamiltonian: $$H_\Lambda = - \mathop \Sigma \limits_{x \in \Lambda } \frac{{h(x)}}{2}\frac{{\partial ^2 }}{{\partial \varphi (x)^2 }} - J\mathop \Sigma \limits_{\left\langle {x,y} \right\rangle \in \Lambda } \cos (\varphi (x) - \varphi (y))$$ , wherex,y∈Z ^d , 〈,〉 denotes nearest neighbors inZ ^d ;J>0 andh={h(x)>0,x∈Z ^d } are independent identically distributed random variables with common distributiondμ(h), satisfying ∫h ^?δ dμ(h)<∞ for some δ>0. We prove that for anym>0 it is possible to chooseJ(m) sufficiently small such that, if 0<J<J(m), for almost every choice ofh and everyx∈Z ^d the ground state correlation function satisfies $$\left\langle {\cos (\varphi (x) - \varphi (y))} \right\rangle \leqq C_{x,h,J} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _x,h,J <∞.     

A generalized reggeon field theory incorporating hard scattering effects

Guided by the parton interpretation of RFT and by QCD, we propose an RFT where the pomeron field depends both onb and onQ ², the bare propagator describing an inhomogenous random walk inb and in lnQ ². Here,Q ² measures the virtuality of the inelastic processes which generate the pomeron exchange amplitude as their shadow. The asymptotic behaviour of such a theory should be different from that of standard RFT, at and above the critical point. Arguments are given in favour of a supercritical pomeron.     

Localization in the ground state of the ising model with a random transverse field

We study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by $$H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} } $$ whereJ>0,x,y∈Z ^d, σ₁, σ₃ are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Z ^d} are independent identically distributed random variables. We consider the ground state correlation function 〈σ₃(x)σ₃(y)〉 and prove:

1. Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Z ^d, that $$\left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle \leqq C_{x,h} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _{x h} <∞.
2. Letd≧2. IfJ is sufficiently large, then, for almost every choice of the random transverse fieldh, the model exhibits long range order, i.e., $$\mathop {\overline {\lim } }\limits_{\left| y \right| \to \infty } \left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle > 0$$ for anyx∈Z ^d.

     

Schrödinger operator with a nonlocal potential whose absolutely continuous and point spectra coexist

We consider the Schrödinger-like operatorH in which the role of a potential is played by the lattice sum of rank 1 operators \(|\left. {v_n } \right\rangle \left\langle {v_n |} \right.\) multiplied by g tan π[(α,n)+ω],g>0, α∈? ^d ,n∈? ^d , ω∈[0, 1]. We show that if the vector α satisfies the Diophantine condition and the Fourier transform support of the functionsv _n (x)=v(x-n),x∈? ^d ,n∈? ^d , is small then the spectrum ofH consists of a dense point component coinciding with? and an absolutely continuous component coinciding with [?, ∞), where ? is the radius of the mentioned support. Besides, we find the integrated density of statesN(λ) (it has a jump at λ=?) and zero temperature a.c. conductivityσ _λ (v), that also has a jump at λ=? and vanishes faster than any power of the external field frequency ν as ν→0 and λ≠?.     

Ising Critical Exponents on Random Trees and Graphs

We study the critical behavior of the ferromagnetic Ising model on random trees as well as so-called locally tree-like random graphs. We pay special attention to trees and graphs with a power-law offspring or degree distribution whose tail behavior is characterized by its power-law exponent τ > 2. We show that the critical inverse temperature of the Ising model equals the hyperbolic arctangent of the reciprocal of the mean offspring or mean forward degree distribution. In particular, the critical inverse temperature equals zero when ${\tau \in (2,3]}$ where this mean equals infinity. We further study the critical exponents δ, β and γ, describing how the (root) magnetization behaves close to criticality. We rigorously identify these critical exponents and show that they take the values as predicted by Dorogovstev et al. (Phys Rev E 66:016104, 2002) and Leone et al. (Eur Phys J B 28:191–197, 2002). These values depend on the power-law exponent τ, taking the same values as the mean-field Curie-Weiss model (Exactly solved models in statistical mechanics, Academic Press, London, 1982) for τ > 5, but different values for ${\tau \in (3,5)}$ .     

Aging effect in CaLaBa{Cu1???xFex}3O7???�� with 0 �� x �� 0.07 studied by M?ssbauer spectroscopy

In this work, we study the long-term aging effect caused by Fe atoms in the superconductor CaLaBa{Cu_1???xFe_x}₃O_7????? with 0 ?? x ?? 0.07. XRD confirms that this system has a YBCO-like structure. The critical temperature (T_c) is strongly affected by aging and depends on the amount of Fe in the structure. Room temperature Mössbauer spectroscopy reveals the presence of the typical species A, B?CB ??, C and new species E ?? and F. Interestingly; A, which corresponds to the Fe^3?+? atom located in the Cu(1) of the chains with spin S _z = 3/2, shows a drastic reduction which means migration to the species B, B ?? and C. Species B and B ?? correspond to the Fe^3?+? in the Cu(2) site forming planar quasi-octahedral and planar square pyramidal, while the C specie is a square pyramidal with O(5) respectively (spin S_z = 3/2 in all these cases). Aging causes loss of superconductivity in the samples with 5 and 7% of iron content.     

The influence of disorder on magnetocaloric effect and the order of transition in ferromagnetic manganite (La1−x Nd x )2/3(Ca1−y Sr y )1/3MnO3

Magnetocaloric effect and order of transition in (La_1?x Nd _x )_2/3(Ca_1?y Sr _y )_1/3MnO₃, prepared by conventional solid-state reaction, have been investigated. Using Banerjee criterion, we demonstrate first-order transition for (J1) and (J2 ) as well as second-order transition for (J3 ), (J4 ), and (J5 ) samples. The ΔS _M ^max is ranging between 9.18 Jkg^?1 K^?1 and 4.87 when Nd and Sr content changes leading to relative cooling power (RCP) varying between 330 and 229.35 J/kg. Both ΔS _M ^max and the RCP are found sensitive to the disorder σ ². The universal behavior obtained from ΔS variation curves confirmed the first-order transition for (J1) and (J2 ) samples and second-order transition for (J3), (J4), and (J5 ) samples obtained by Banerjee criterion. All samples with second-order phase transition exhibit inhomogeneous character estimated from local exponent n.     

Noncollective oblate states in 113Te

High-spin states of 113Te were studied by in-beam spectroscopy using the 88Sr (28Si, 3n) fusion-evaporation reaction at a beam energy of 120 MeV. 7-7, charged particle-7-7 coincidences, and 7-7 angular correlation analyses were employed for determining the level scheme of 113Te. The levels based on the 11/2 - state in 113Te were identified for the first time. The present result of the level scheme of 113Te was in accord with the systematics of those in the heavier isotopes, namely 115Te and 117Te. A particularly favoured 37/2+ state was observed and suggested to be the fully aligned noncollective oblate 7r[(g9/2)2]6+ <8)^[(^5/2) <8s> (h 11/2)2]25/2+ configuration.     

Kauffman Cellular Automata on Quasicrystal Topology

In this paper, we perform numerical simulations to study Kauffman cellular automata (KCA) on quasiperiod lattices. In particular, we investigate phase transition, magnetic entropy, and propagation speed of the damage on these lattices. Both the critical threshold parameter \(p_{c}\) and the critical exponents are estimated with good precision. In order to investigate the increase of statistical fluctuations and the onset of chaos in the critical region of the model, we have also defined a magnetic entropy to these systems. It is seen that the magnetic entropy behaves in a different way when one passes from the frozen regime (p < p_c) to the chaotic regime (p > p_c). For a further analysis, the robustness of the propagation of failures is checked by introducing a quenched site dilution probability q on the lattices. It is seen that the damage spreading is quite sensitive when a small fraction of the lattice sites are disconnected. A finite-size scaling analysis is employed to estimate the critical exponents. From these numerical estimates, we claim that on both pure (q =?0) and diluted (q =?0.05) quasiperiodic lattices, the KCA model belongs to the same universality class than on square lattices. Furthermore, with the aim of comparing the dynamical behavior between periodic and quasiperiodic systems, the propagation speed of the damage is also calculated for the square lattice assuming the same conditions. It is found that on square lattices the propagation speed of the damage obeys a power law as \(v\sim (p-p_{c})^{\alpha }\), whereas on quasiperiod lattices, it follows a logarithmic law as \(v \sim \ln (p-p_{c})^{\alpha }\).     

Truncated Connectivities in a Highly Supercritical Anisotropic Percolation Model

We consider an anisotropic bond percolation model on $\mathbb{Z}^{2}$ , with p=(p _h ,p _v )∈[0,1]², p _v >p _h , and declare each horizontal (respectively vertical) edge of $\mathbb{Z}^{2}$ to be open with probability p _h (respectively p _v ), and otherwise closed, independently of all other edges. Let $x=(x_{1},x_{2}) \in\mathbb{Z}^{2}$ with 0<x ₁<x ₂, and $x'=(x_{2},x_{1})\in\mathbb{Z}^{2}$ . It is natural to ask how the two point connectivity function $\mathbb{P}_{\mathbf{p}}(\{0\leftrightarrow x\})$ behaves, and whether anisotropy in percolation probabilities implies the strict inequality $\mathbb{P}_{\mathbf{p}}(\{0\leftrightarrow x\})>\mathbb{P}_{\mathbf {p}}(\{0\leftrightarrow x'\})$ . In this note we give an affirmative answer in the highly supercritical regime.     

Localization for a Random Walk in Slowly Decreasing Random Potential

We consider a continuous time random walk X in a random environment on ?⁺ such that its potential can be approximated by the function V:?⁺→? given by $V(x)=\sigma W(x) -\frac {b}{1-\alpha}x^{1-\alpha}$ where σW a Brownian motion with diffusion coefficient σ>0 and parameters b, α are such that b>0 and 0<α<1/2. We show that P-a.s. (where P is the averaged law) $\lim_{t\to\infty} \frac{X_{t}}{(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}}=1$ with $C^{*}=\frac{2\alpha b}{\sigma^{2}(1-2\alpha)}$ . In fact, we prove that by showing that there is a trap located around $(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}$ (with corrections of smaller order) where the particle typically stays up to time t. This is in sharp contrast to what happens in the “pure” Sinai’s regime, where the location of this trap is random on the scale ln² t.     

Decay of helicity in homogeneous turbulence

The self-similar relaxation of helicity in homogeneous turbulence has been considered taking into account integral invariants ∫ ₀ ^∞ r ^m 〈u(x)ω(x + r)〉 dr = I _m ^h (where ω = curlu and r = |r|). It has been shown that integral invariants with m = 3 for both helicity and energy are possible in addition to helical analogs of Loitsyanskii (m = 4) and Birkhoff-Saffman (m = 2) invariants associated with the conservation laws of momentum and angular momentum, respectively. Helicity always relaxes more rapidly than the energy. Its decay exponent is in the interval from ?3/2 to ?5/2 versus the interval from ?6/5 to ?10/7 for the energy.     

T-odd correlations in (n, αγ) reactions

The T-odd correlation (k _α · [σ × k _γ])(k _α · k _γ), where σ is the vector of the neutron polarization and the symbols k denote the respective linear momenta (all vectors are unit ones), in the sequential alpha-gamma cascade induced by a thermal-neutron capture is studied. The study is performed in the one-resonance approximation. Both the final-state interaction of the alpha particle with the residual nucleus and the actual T-noninvariant phase shift are considered as possible origins of the correlation. The problem of suitable target isotopes is analyzed. Related correlations in other neutron- and proton-induced reactions are discussed.     

Electron spectral functions of two-dimensional high-T c superconductors in the model of fermion condensation

Spectral functions of strongly correlated two-dimensional (2D) electron systems in solids are studied on the assumption that these systems undergo a phase transition, called fermion condensation, whose characteristic feature is flattening of the electron spectrum ε(p). Unlike the previous models, the decay of single-particle states in our study is properly taken into account. Results of our calculations are shown to be in qualitative agreement with ARPES data. The universal behavior of the ratio ImΣ(p, ε, T)/T as a function of x=ε/T, uncovered in [3] for the single-particle states around the diagonal of the Brillouin zone, are found to be reproduced reasonably well. However, in our model this behavior is destroyed in vicinities of the van Hove points, where the fermion condensate resides.     

Electromagnetic induction in conductors accelerated in magnetic fields amplified by flux compression

The initial boundary-value problem for the electromagnetic induction in a conducting slab ats(t)≦x≦s(t)+a resulting from its accelerated motionv={s(t), 0, 0} across a transverse magnetic fieldB={0,B(x,t), 0} is treated, when the latter is amplified by orders-of-magnitude with respect to its initial valueB(x,t=0)=B ₀(x) by flux compression in the gap between the moving conductor surfacex=s(t) and an ideal resting conductor atx=0. Two initial (t=0) configurations are considered, assuming that (I)B ₀ (step-shaped) has not yet and (II)B ₀ (uniform) has completely diffused into the conductor atx=s(t=0). By means of a time-dependent coordinate transformation ξ=[x ? s(t)]/a and Fourier series expansions, the electromagnetic fields in the moving conductor are represented as integralfunctionals of the magnetic fieldB ₁ (t) in the gap 0≦x≦s(t).B ₁ (t) is given analytically as solution of a singular Volterra integro-differential equation. The theory is valid for arbitrary (nonrelativistic) speeds.(t) and accelerationss(t)) of the moving conductor. Applications to explosion driven electric induction generators and magnetic flux experiments are discussed briefly.     

The Percolation Transition in the Zero-Temperature Domany Model

We analyze a deterministic cellular automaton σ ^?=(σ ⁿ :n≥0) corresponding to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice $\mathbb{N}$ . The state space $\mathcal{S}_\mathbb{H} = \left\{ { - 1, + 1} \right\}^\mathbb{H}$ consists of assignments of ?1 or +1 to each site of $\mathbb{H}$ and the initial state $\sigma ^0 = \left\{ {\sigma _{^x }^0 } \right\}_{x \in \mathbb{H}}$ is chosen randomly with P(σ ⁰ _x=+1)=p∈[0,1]. The sites of $\mathbb{H}$ are partitioned in two sets $\mathcal{A}$ and $\mathcal{B}$ so that all the neighbors of a site x in $\mathcal{A}$ belong to $\mathcal{B}$ and vice versa, and the discrete time dynamics is such that the σ ^? _x 's with ${x \in \mathcal{A}}$ (respectively, $\mathcal{B}$ ) are updated simultaneously at odd (resp., even) times, making σ ^? _x agree with the majority of its three neighbors. In ref. 1 it was proved that there is a percolation transition at p=1/2 in the percolation models defined by σ ⁿ , for all times n∈[1,∞]. In this paper, we study the nature of that transition and prove that the critical exponents β, ν, and η of the dependent percolation models defined by σ ⁿ , n∈[1,∞], have the same values as for standard two-dimensional independent site percolation (on the triangular lattice).     

Magnetic and electronic properties of Cr- and Mn-doped SnO2: ab initio calculations

The ab initio calculations, based on the Korringa–Kohn–Rostoker (KKR) approximation method combined with the coherent potential approximation (CPA), indicated as KKR–CPA, have been used to study the stability of ferromagnetic and ferrimagnetic states, for systems that are SnO₂ doped and co-doped with two transition metals, that is, chromium and manganese. Our results indicate that the ferromagnetic state is more stable than the spin-glass state for the (Sn_1−xCr_xO₂; x = 0.07, 0.09, 0.12 and 0.15)-doped system, while the spin-glass state is more stable than the ferromagnetic state for the (Sn_1−xMn_xO₂; x = 0.02 and 0.05)-doped system. However, the ferromagnetic and/or the ferrimagnetic states are stable for the (Sn_0.98−xMn_0.02Cr_xO₂; x = 0.05, 0.09 and 0.13)-doped system depending on the Cr concentration. Moreover, we estimated the Curie temperature (T_c) for the Cr-doped tin dioxide (SnO₂), and we explained the origin of magnetic behaviour through the total density of states for different doped and co-doped SnO₂ systems.