On the damage spreading in Ising spin glasses

The spreading of the Hamming distance or damage has been investigated for ±J Ising spin glasses under heat bath dynamics. Dimensions d = 2, 3, 4, 6 and mean field were studied. For finite dimensions, the damage goes to zero at long times above a temperature T_D(d). Accurate values of this critical temperature were obtained, together with certain critical exponents. The spin glass ordering temperatures T_g were also estimated from the damage spreading data. The results are compared with other work and discussed from a phase space approach.     

Spin glass behaviour of the spinel system GexCu1−xFe2O4

Ac-susceptibility measurements at various temperatures and hysteresis studies at various fields indicate that the system Ge_xCu_1?xFe₂O₄ (x ? 0.6) contains mixed multidomain, single domain or superparamagnetic states. Sharp susceptibility maxmima, resembling those of spin glasses, are observed for x = 0.1 and 0.2, which may be attributed to the single domain-superparamagnetic (SDSP) transition and the overall behaviour shows a cluster spin glass type of ordering.     

Variational approach for the N-state spin and gauge Potts model

A hamiltonian variational treatment is applied both to the spin Potts model and to its gauge version for any number of states N and spatial dimensions d?2. Regarding the former we reproduce the correct critical coupling and latent heat for not too low N and d. For the latter, our approach turns the gauge theory into an equivalent d-dimensional classical spin model, which evaluated for d + 1 = 4 gives results in agreement with 1/N expansions.     

On the upper critical dimensions of random spin systems

A set of critical exponent inequalities is proved for a large class of classical random spin systems. The inequalities imply rigorous (and probably the optimal) lower bounds for the upper critical dimensions, i.e.,d _u4 for regular and random ferromagnets,d _u6 for spin glasses and random field systems.     

Gravitational anomalies

It is shown that in certain parity-violating theories in 4k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of $\text{spin}\text{-}\text{1}\text{2}\text{or}\text{-3}\text{2}$ or self-dual antisymmetric tensor fields are coupled to gravity. (For Dirac fermions there is no trouble.) The conditions for anomaly cancellation between fields of different spin is investigated. In six dimensions this occurs in certain theories with a fairly elaborate field content. In ten dimensions there is a unique theory with anomaly cancellation between fields of different spin. It is the chiral n = 2 supergravity theory, which is the low-energy limit of one of the superstring theories. Beyond ten dimensions there is no way to cancel anomalies between fields of different spin.     

Geometrical string and dual spin systems

We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a two-plaquette gauge hamiltonian. The duality transformation is constructed in geometrical and algebraic language. The dual hamiltonian represents a new type of spin system with local gauge invariance. At each vertex ξ there are d (d − 1) /2 Ising spins ∧_{μ, η} = ∧_{η,μ N}. ≠ P = 1, … , d and one Ising spin Γ on every linkξ ξ + e,). For the frozen spin Γ  1 the dual hamiltonian factorizes into d (d − 1) /2 two-dimensional Ising ferromagnets and into antiferromagnets in the case Γ  −1. For fluctuating F it is a sort of spin-glass system with local gauge invariance. The generalization to p-membranes is given.     

Large q expansions for q-state gauge-matter Potts models in lagrangian form

We consider the lagrangian form of a q-state generalization of Ising gauge theories with matter fields in d = 3 and 4 dimensions. The theory is exactly soluble in the limit q → ∞ and corrections are easily calculable in power series in $\text{1}\text{q}{}^{\mathrm{<mtext>1</mtext><mtext>d</mtext>}}$. Extrapolating the series for the free energies and latent heats by the method of Padé approximants, we have constructed the phase diagrams for all values of q. Our results agree well with known results for pure spin systems and, for the case q = 2, with Ising Monte Carlo data.     

Discrete symmetries in Kaluza-Klein theories

We investigate discrete symmetries in theories of higher-dimensional (d > 4) gravity and their consequences for the reduced four-dimensional theory, obtained for a ground state which is a direct product of four-dimensional Minkowski space and a compact d ? 4 dimensional internal space. If the action of pure d-dimensional gravity coupled to spinors is invariant under time reversal or reflection of an odd number of spacelike co-ordinates, the reduced four-dimensional theory has a non-trivial parity or CT symmetry not consistent with observation. A non-trivial d-dimensional charge conjugation results in an unwanted doubling of the four-dimensional fermion spectrum. As a consequence, realistic theories can only be obtained for Majorana-Weyl spinors in d = 2 mod 8 dimensions. The constraints are less stringent if supplementary fields are introduced in d dimensions. For d = 11 supergravity, for example, parity and CT invariance can be broken by a non-vanishing field strength of the totally antisymmetric three-index tensor.A ground state invariant under reflections of “internal” co-ordinates often gives rise to a non-trivial charge conjugation in four dimensions. We find that the ground state of a realistic Kaluza-Klein theory should not be invariant under any non-trivial internal co-ordinate reflection (which cannot be obtained by a gauge transformation). We finally comment on a possible solution of the strong-CP problem from Kaluza-Klein theories and discuss prospectives for finding internal spaces admitting chiral fermions.     

Quark trapping for lattice U(1) gauge fields

We show for lattice U(1) gauge fields in d = 3 dimensions, that 〈exp(i∮_CAdx)〉 ? exp (? const.T lnL), where C is a rectangle of dimension T × L, T ? L. This indicates quark trapping, by a potential at least as strong as Coulomb.     

The magnetic phase diagram of amorphous FexPd82−xSi18, 2⩽x⩽25

The magnetic phase diagram of the metallic glasses Fe_xPd_82?xSi₁₈, 2?x?25, is presented. Transitions from spin glass to weak ferromagnetism with composition and temperature are associated with the composition dependent heterogeneity of the rapidly quenched materials.     

Chirality index and dimensional reduction of fermions

The number of four-dimensional chiral fermions obtained from dimensional reduction of models with spinor matter fields coupled to pure gravity in d > 4 dimensions is linked to topological properties of the internal d ? 4 dimensional space. This gives important restrictions on possible ground states of such models consistent with a realistic four-dimensional unified theory. Connections with spontaneous symmetry breaking and Yukawa couplings of fermions in unified theories are discussed.     

Local spin configurations of Fe atoms in the Rh1−x Fex (x=0.1, 0.2, and 0.3) system with competing exchange interactions

The local spin configurations of Fe atoms in the magnetically ordered alloys Rh_1?x Fe_x (x=0.1, 0.2, and 0.3) have been investigated by Mössbauer spectroscopy. The Mössbauer absorption spectra are measured in the range from 5 K to temperatures of the transition to the paramagnetic state. The measurements in magnetic fields with a strength up to 5 T are carried out at a temperature of 4.2 K. Analysis of the magnetic-hyperfinefield distribution functions demonstrates that Fe atoms form discrete sets of collinear spin configurations corresponding to different net moments of the nearest coordination sphere. The spin structure of the alloys is governed by a random distribution of Fe atoms over the lattice sites and the competition between the Fe-Rh ferromagnetic exchange interaction and the antiferromagnetic interaction of the neighboring Fe atoms. No spin frustration and spin “melting” effects characteristic of spin glasses are revealed in the Rh-Fe alloys.     

Dimensional reduction of Weyl,Majorana and Majorana-Weyl spinors

We discuss the dimensional reduction for Weyl, Majorana, or Majorana-Weyl spinors coupled to pure d-dimensional (d ? 4) gravity. The only case where a realistic four-dimensional low-energy spectrum for the fermions may be obtained, is for a Majorana-Weyl spinor in d = 2 mod 8 dimensions. Chiral massless fermions are not excluded in this case. The minimal number of dimensions for the construction of a realistic theory out of pure gravity is d = 18.     

On the p-spin interaction transverse Ising spin-glass model without replicas

The p-spin interaction Ising spin glass model in the presence of a transverse field is studied in the large p-limit by means of a convenient operator extension of the cavity fields method avoiding replicas and the Trotter-Suzuki transformation. The results appear quite consistent with those recently obtained for the same model using conventional treatments within the replica trick. This gives additional support to the cavity fields approach as a promising tool towards a general theory of classical and quantum spin glasses.     

A full potential all-electron calculation on electronic structure of NiO

We perform a first principle calculation on NiO system, a prototypical correlated electronic system due to partial filled 3d electronic shell, using various density functional theory (DFT) and hybrid functional methods inclusion of spin polarization (SP), on-site Coulomb repulsion U and spin–orbit coupling (SOC) effects. It is shown that localized spin density approximation (LSDA) plus U (LSDA?+?U) correctly reproduce experimental lattice parameter, while spin polarization generalized gradient approximation (SP?+?GGA?+?U) obviously overestimates lattice parameter. LSDA?+?U/SP?+?GGA?+?U band gaps and magnetic moments are in agreement with experimental data, and correctly predict NiO to be an insulator. NiO undergoes a Mott–Hubbard metal–insulator transition (MIT) by addition of Coulomb interaction U. Our LSDA?+?SOC calculation shows that SOC further splitting of Ni d e_g and t_2g orbitals into d_z2, d_xy, d_x2y2 and d_xz?+?d_yz orbitals, and SP nearly cancels out SOC effect, giving rise to symmetry of density of states (DOS) for spin-up and spin-down states, hence appearance of zero net magnetic moment. For LSDA?+?U?+?SOC calculation, combination effect of SP, U and SOC results in non-occupying of spin-up conduction band and a negligible density of states for spin-down states.     

Continuous matter fields in Regge calculus

We find that the continuous matter fields are ill-defined in Regge calculus in the physical 4D theory since the corresponding effective action has infinite terms unremovable by the UV renormalisation procedure. These terms are connected with the singular nature of the curvature distribution in Regge calculus, namely, with the presence in d>2 dimensions of the (d−3)-dimensional simplices where the (d−2)-dimensional ones carrying different conical singularities are meeting. Possible resolution of this difficulty is discretisation of matter fields in Regge background.     

Quantum critical behavior of the Kondo necklace model with aperiodic exchange modulation

The low energy behavior of the Kondo necklace model with an aperiodic exchange modulation is studied using a representation for the localized and conduction electron spins, in terms of local Kondo singlet and triplet operators at zero and finite temperature for arbitrary d dimensions. A decoupling scheme on the double time Green's functions is used to find the dispersion relation for the excitations of the system. We determined the dependence between the chemical aperiodic exchange modulation and the spin gap in 1d, 2d and 3d, at zero temperature and in the paramagnetic side of the phase diagram. On the other hand, at low but finite temperatures, the line of Néel transitions in the antiferromagnetic phase is calculated in function of the aperiodic exchange modulation.     

Absence of symmetry breaking forN-vector spin glass models in two dimensions

We prove the absence of continuous symmetry breaking at arbitrary temperatures for two-dimensionalN-vector spin glass models with Hamilton function $$H = - \sum\limits_{i,j} {J(i,j)\left| {i - j} \right|^{ - 2 - \varepsilon } S_i \cdot S_j ,} \varepsilon > 0$$ whereJ (i, j) has mean 0 and variance 1, for alli, j. We comment on the role of boundary conditions in spin glasses and on their critical behaviour in high dimensions.     

On the susceptibility exponent of random anisotropy magnets

The temperature dependence of the non-linear susceptibility ≈₂(T) of random anisotropy magnets in the Ising limit (speromagnets) is calculated for temperatures above the freezing temperature T_f within the framework of the correlated molecular field theory. For the effective susceptibility exponent λ_s(T) = (T?T_f)≈₂d^-1_≈2/dT a non-monotonic temperature dependence is found as for the case of spin glasses. This must be taken into account in order to obtain reliable values for the critical susceptibility exponent from experimental data.     

Replica symmetry breaking in and around six dimensions

Two, replica symmetry breaking specific, quantities of the Ising spin glass — the breakpoint x₁ of the order parameter function and the Almeida-Thouless line — are calculated in six dimensions (the upper critical dimension of the replicated field theory used), and also below and above it. The results confirm that replica symmetry breaking does exist below d=6, and also the tendency of its escalation for decreasing dimension continues. As a new feature, x₁ has a nonzero and universal value for d<6 at criticality. Near six dimensions we have x1c=3(6−d)+O[²(6−d)]. A method to expand a generic theory with replica equivalence around the replica symmetric one is also demonstrated.