Structural precursor to freezing: An integral equation study

Recent simulation studies have drawn attention to the shoulder which forms in the second peak of the radial distribution function of hard-spheres at densities close to freezing and which is associated with local crystalline ordering in the dense fluid. We address this structural precursor to freezing using an inhomogeneous integral equation theory capable of describing local packing constraints to a high level of accuracy. The addition of a short-range attractive interaction leads to a well known broadening of the fluid-solid coexistence region as a function of attraction strength. The appearence of a shoulder in our calculated radial distribution functions is found to be consistent with the broadened coexistence region for a simple model potential, thus demonstrating that the shoulder is not exclusively a high density packing effect

Probing spatial spin correlations of ultracold gases by quantum noise spectroscopy

Spin noise spectroscopy with a single laser beam is demonstrated theoretically to provide a direct probe of the spatial correlations of cold fermionic gases. We show how the generic many-body phenomena of anti-bunching, pairing, antiferromagnetic, and algebraic spin liquid correlations can be revealed by measuring the spin noise as a function of laser width, temperature, and frequency.Comment: Revised version. 4 pages, 3 figures. Accepted for PR

Statistical mechanical description of liquid systems in electric field

We formulate the statistical mechanical description of liquid systems for both polarizable and polar systems in an electric field in the $\mathbf{E}$-ensemble, which is the pendant to the thermodynamic description in terms of the free energy at constant potential. The contribution of the electric field to the configurational integral $\tilde{Q}_{N}(\mathbf{E})$ in the $\mathbf{E}$-ensemble is given in an exact form as a factor in the integrand of $\tilde{Q}_{N}(\mathbf{E})$. We calculate the contribution of the electric field to the Ornstein-Zernike formula for the scattering function in the $\mathbf{E}$-ensemble. As an application we determine the field induced shift of the critical temperature for polarizable and polar liquids, and show that the shift is upward for polarizable liquids and downward for polar liquids.Comment: 6 page

Low temperature series expansions for the square lattice Ising model with spin S > 1

We derive low-temperature series (in the variable $u = \exp[-\beta J/S^2]$) for the spontaneous magnetisation, susceptibility and specific heat of the spin-$S$ Ising model on the square lattice for $S=\frac32$, 2, $\frac52$, and 3. We determine the location of the physical critical point and non-physical singularities. The number of non-physical singularities closer to the origin than the physical critical point grows quite rapidly with $S$. The critical exponents at the singularities which are closest to the origin and for which we have reasonably accurate estimates are independent of $S$. Due to the many non-physical singularities, the estimates for the physical critical point and exponents are poor for higher values of $S$, though consistent with universality.Comment: 14 pages, LaTeX with IOP style files (ioplppt.sty), epic.sty and eepic.sty. To appear in J. Phys.

Weakly frustrated two-dimensional Heisenberg antiferromagnets: thermodynamic properties from a non-perturbative approach

We analyze the thermodynamic properties of the spin-S two-dimensional quantum Heisenberg antiferromagnet on a square lattice with nearest and next-nearest neighbor couplings in the Neel phase (J_2/J_1<0.4) employing the quantum hierarchical reference theory (QHRT), a non-perturbative implementation of the renormalization group method to quantum systems. We investigate the staggered susceptibility, the structure factors and the correlation length at finite temperature and for different values of the frustration ratio. From the finite temperature results, we also extrapolate ground state properties, such as spin stiffness and spontaneous staggered magnetization, providing an estimate of the extent of quantum corrections. The behavior of these quantities as a function of frustration may provide some hint on the breakdown of the Neel phase at zero temperature for larger values of J_2

Anisotropy effects in a mixed quantum-classical Heisenberg model in two dimensions

We analyse a specific two dimensional mixed spin Heisenberg model with exchange anisotropy, by means of high temperature expansions and Monte Carlo simulations. The goal is to describe the magnetic properties of the compound (NBu_{4})_{2}Mn_{2}[Cu(opba)]_{3}\cdot 6DMSO\cdot H_{2}O which exhibits a ferromagnetic transition at $T_{c}=15K$. Extrapolating our analysis on the basis of renormalisation group arguments, we find that this transition may result from a very weak anisotropy effect.Comment: 8 pages, 10 Postscript figure

Magnetic Order and Dynamics in an Orbitally Degenerate Ferromagnetic Insulator

Neutron scattering was used to determine the spin structure and the magnon spectrum of the Mott--Hubbard insulator YTiO$_3$. The magnetic structure is complex, comprising substantial G-type and A-type antiferromagnetic components in addition to the predominant ferromagnetic component. The magnon spectrum, on the other hand, is gapless and nearly isotropic. We show that these findings are inconsistent with the orbitally ordered states thus far proposed for YTiO$_3$ and discuss general implications for a theoretical description of exchange interactions in orbitally degenerate systems.Comment: to appear in Phys. Rev. Let

Phase transition in a 2-dimensional Heisenberg model

We investigate the two-dimensional classical Heisenberg model with a nonlinear nearest-neighbor interaction V(s,s')=2K[(1+s.s')/2 ]^p. The analogous nonlinear interaction for the XY model was introduced by Domany, Schick, and Swendsen, who find that for large p the Kosterlitz-Thouless transition is preempted by a first-order transition. Here we show that, whereas the standard (p=1) Heisenberg model has no phase transition, for large enough p a first-order transition appears. Both phases have only short range order, but with a correlation length that jumps at the transition.Comment: 6 pages, 5 encapsulated postscript figures; to appear in Physical Review Letter

Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the Tb2Ti2O7, pyrochlore antiferromagnet

Highly frustrated antiferromagnets composed of magnetic rare-earth moments are currently attracting much experimental and theoretical interest. Rare-earth ions generally have small exchange interactions and large magnetic moments. This makes it necessary to understand in detail the role of long-range magnetic dipole-dipole interactions in these systems, in particular in the context of spin-spin correlations that develop in the paramagnetic phase, but are often unable to condense into a conventional long-range magnetic ordered phase. This scenario is most dramatically emphasized in the frustrated pyrochlore antiferromagnet material Tb2Ti207 which does not order down to 50 mK despite an antiferromagnetic Curie-Weiss temperature Tcw ~ -20 K. In this paper we report results from mean-field theory calculations of the paramagnetic elastic neutron-scattering in highly frustrated magnetic systems with long-range dipole-dipole interactions, focusing on the Tb2Ti207 system. Modeling Tb2Ti207 as an antiferromagnetic Ising pyrochlore, we find that the mean-field paramagnetic scattering is inconsistent with the experimentally observed results. Through simple symmetry arguments we demonstrate that the observed paramagnetic correlations in Tb2Ti207 are precluded from being generated by any spin Hamiltonian that considers only Ising spins, but are qualitatively consistent with Heisenberg-like moments. Explicit calculations of the paramagnetic scattering pattern for both Ising and Heisenberg models, which include finite single-ion anisotropy, support these claims. We offer suggestions for reconciling the need to restore spin isotropy with the Ising like structure suggested by the single-ion properties of Tb3+.Comment: Revtex4, 18 pages, 3 eps figures (2 color figures). Change in title and emphasis on Tb2Ti2O7 only. Spin-ice material removed, to appear in a later publicatio

Spin versus Lattice Polaron: Prediction for Electron-Doped CaMnO3

CaMnO3 is a simple bi-partite antiferromagnet(AF) which can be continuously electron-doped up to LaMnO3. Electrons enter the doubly degenerate E_g subshell with spins aligned to the S=3/2 core of Mn^4+ (T_2g^3)$. We take the Hubbard and Hund energies to be effectively infinite. Our model Hamiltonian has two E_g orbitals per Mn atom, nearest neighbor hopping, nearest neighbor exchange coupling of the S=3/2 cores, and electron-phonon coupling of Mn orbitals to adjacent oxygen atoms. We solve this model for light doping. Electrons are confined in local ferromagnetic (FM) regions (spin polarons) where there proceeds an interesting competition between spin polarization (spin polarons) which enlarges the polaron, and lattice polarization (Jahn-Teller polarons) which makes it smaller. A symmetric 7-atom ferromagnetic cluster (Mn_7^27+) is the stable result, with net spin S=2 relative to the undoped AF. The distorted oxygen positions around the electron are predicted. The model also predicts a critical doping x_c=0.045 where the polaronic insulator becomes unstable relative to a FM metal.Comment: 9 pages with 7 embedded postscript figures and 2 table