Long-range and short-range magnetic correlations, and microscopic origin of net magnetization in the spin-1 trimer chain compound CaNi3P4O14

Spin-spin correlations and microscopic origin of net magnetization in the spin-1 trimer chain compound CaNi3P4O14 have been investigated by powder neutron diffraction. The present study reveals a 3D long-range magnetic ordering below 16 K where the magnetic structure consists of ferromagnetic trimers that are coupled ferromagnetically along the spin-chain. The moment components along the a and c axes arrange antiferromagnetically. Our study establishes that the uncompensated moment components along the b axis result in a net magnetization per unit cell. The magnetic structure, determined in the present study, is in agreement with the results of recent first principles calculation; however, it is in contrast to a fascinating experimental prediction of ferrimagnetic ordering based on the periodicity of the exchange interactions in CaNi3P4O14. Our study also confirms the presence of broad diffuse magnetic scattering, due to 1D short-range spin-spin correlations, over a wide temperature range below ~50 K down to a temperature well below the Tc. Total neutron scattering analysis by the RMC method reveals that the dominating spin-spin correlation above Tc is ferromagnetic and along the b axis. The nearest neighbour spin-spin correlations along the a and c axes are found to be weakly antiferromagnetic. The nature of the trimer spin structure of the short-range state is similar to that of the 3D long-range ordered state. The present investigation of microscopic nature of the magnetic ground state also explains the condition required for the 1/3 magnetization plateau to be observed in the trimer spin-chains. In spite of the S=1 trimer chain system, the present compound CaNi3P4O14 is found to be a good realization of 3D magnet below the Tc=16 K with full ordered moment values of ~2 mu_B/Ni2+ (1.98 and 1.96 mu_B/Ni2+ for two Ni sites, respectively) at 1.5 K.Comment: 10 pages, 8 figure

The replica symmetric behavior of the analogical neural network

In this paper we continue our investigation of the analogical neural network, paying interest to its replica symmetric behavior in the absence of external fields of any type. Bridging the neural network to a bipartite spin-glass, we introduce and apply a new interpolation scheme to its free energy that naturally extends the interpolation via cavity fields or stochastic perturbations to these models. As a result we obtain the free energy of the system as a sum rule, which, at least at the replica symmetric level, can be solved exactly. As a next step we study its related self-consistent equations for the order parameters and their rescaled fluctuations, found to diverge on the same critical line of the standard Amit-Gutfreund-Sompolinsky theory.Comment: 17 page

Graphene via large N I: Renormalization

We analyze the competing effects of moderate to strong Coulomb electron-electron interactions and weak quenched disorder in graphene. Using a one-loop renormalization group calculation controlled within the large-N approximation, we demonstrate that, at successively lower energy (temperature or chemical potential) scales, a type of non-Abelian vector potential disorder always asserts itself as the dominant elastic scattering mechanism for generic short-ranged microscopic defect distributions. Vector potential disorder is tied to both elastic lattice deformations ("ripples") and topological lattice defects. We identify several well-defined scaling regimes, for which we provide scaling predictions for the electrical conductivity and thermopower, valid when the inelastic lifetime due to interactions exceeds the elastic lifetime due to disorder. Coulomb interaction effects should figure strongly into the physics of suspended graphene films, where rs > 1; we expect vector potential disorder to play an important role in the description of transport in such films.Comment: 25 pages, 21 figure

Statistical mechanics of temporal association in neural networks with transmission delays

We study the representation of static patterns and temporal sequences in neural networks with signal delays and a stochastic parallel dynamics. For a wide class of delay distributions, the asymptotic network behavior can be described by a generalized Gibbs distribution, generated by a novel Lyapunov functional for the determination dynamics. We extend techniques of equilibrium statistical mechanics so as to deal with time-dependent phenomena, derive analytic results for both retrieval quality and storage capacity, and compare them with numerical simulations

Statistical properties of an ensemble of vortices interacting with a turbulent field

We develop an analytical formalism to determine the statistical properties of a system consisting of an ensemble of vortices with random position in plane interacting with a turbulent field. We calculate the generating functional by path-integral methods. The function space is the statistical ensemble composed of two parts, the first one representing the vortices influenced by the turbulence and the second one the turbulent field scattered by the randomly placed vortices.Comment: Third version; Important corrections in the normalization for the gas of vortices, et

Quark Number Fluctuations in a Chiral Model at Finite Baryon Chemical Potential

We discuss the net quark and isovector fluctuations as well as off-diagonal quark flavor susceptibilities along the chiral phase transition line in the Nambu--Jona-Lasinio (NJL) model. The model is formulated at non-zero quark and isospin chemical potentials with non-vanishing vector couplings in the iso-scalar and iso-vector channels. We study the influence of the quark chemical potential on the quark flavour susceptibilities in detail and the dependence of the results on model parameters as well as on the quark mass. The NJL model findings are compared with recent lattice results obtained in two--flavor QCD at finite chemical potential. On a qualitative level, the NJL model provides a consistent description of the dependence of quark number fluctuations on temperature and baryon chemical potential. The phase diagram and the position of the tricritical point in the NJL model are also discussed for different parameter sets.Comment: 33 pages, 11 figures; final version accepted for publication in Phys. Rev.

Dimensional crossover in dipolar magnetic layers

We investigate the static critical behaviour of a uniaxial magnetic layer, with finite thickness L in one direction, yet infinitely extended in the remaining d dimensions. The magnetic dipole-dipole interaction is taken into account. We apply a variant of Wilson's momentum shell renormalisation group approach to describe the crossover between the critical behaviour of the 3-D Ising, 2-d Ising, 3-D uniaxial dipolar, and the 2-d uniaxial dipolar universality classes. The corresponding renormalisation group fixed points are in addition to different effective dimensionalities characterised by distinct analytic structures of the propagator, and are consequently associated with varying upper critical dimensions. While the limiting cases can be discussed by means of dimensional epsilon expansions with respect to the appropriate upper critical dimensions, respectively, the crossover features must be addressed in terms of the renormalisation group flow trajectories at fixed dimensionality d.Comment: 25 pages, Latex, 12 figures (.eps files) and IOP style files include

Microcanonical finite-size scaling in specific heat diverging 2nd order phase transitions

A Microcanonical Finite Site Ansatz in terms of quantities measurable in a Finite Lattice allows to extend phenomenological renormalization (the so called quotients method) to the microcanonical ensemble. The Ansatz is tested numerically in two models where the canonical specific-heat diverges at criticality, thus implying Fisher-renormalization of the critical exponents: the 3D ferromagnetic Ising model and the 2D four-states Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows to simulate systems as large as L=1024 (Potts) or L=128 (Ising). The quotients method provides extremely accurate determinations of the anomalous dimension and of the (Fisher-renormalized) thermal $\nu$ exponent. While in the Ising model the numerical agreement with our theoretical expectations is impressive, in the Potts case we need to carefully incorporate logarithmic corrections to the microcanonical Ansatz in order to rationalize our data.Comment: 13 pages, 8 figure

Defect fugacity, Spinwave Stiffness and T_c of the 2-d Planar Rotor Model

We obtain precise values for the fugacities of vortices in the 2-d planar rotor model from Monte Carlo simulations in the sector with {\em no} vortices. The bare spinwave stiffness is also calculated and shown to have significant anharmonicity. Using these as inputs in the KT recursion relations, we predict the temperature T_c = 0.925, using linearised equations, and $T_c = 0.899 \pm >.005$ using next higher order corrections, at which vortex unbinding commences in the unconstrained system. The latter value, being in excellent agreement with all recent determinations of T_c, demonstrates that our method 1) constitutes a stringent measure of the relevance of higher order terms in KT theory and 2) can be used to obtain transition temperatures in similar systems with modest computational effort.Comment: 7 pages, 4 figure