Efficient calculation of the antiferromagnetic phase diagram of the 3D Hubbard model

The Dynamical Cluster Approximation with Betts clusters is used to calculate the antiferromagnetic phase diagram of the 3D Hubbard model at half filling. Betts clusters are a set of periodic clusters which best reflect the properties of the lattice in the thermodynamic limit and provide an optimal finite-size scaling as a function of cluster size. Using a systematic finite-size scaling as a function of cluster space-time dimensions, we calculate the antiferromagnetic phase diagram. Our results are qualitatively consistent with the results of Staudt et al. [Eur. Phys. J. B 17 411 (2000)], but require the use of much smaller clusters: 48 compared to 1000

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

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

The 1/D Expansion for Classical Magnets: Low-Dimensional Models with Magnetic Field

The field-dependent magnetization m(H,T) of 1- and 2-dimensional classical magnets described by the $D$-component vector model is calculated analytically in the whole range of temperature and magnetic fields with the help of the 1/D expansion. In the 1-st order in 1/D the theory reproduces with a good accuracy the temperature dependence of the zero-field susceptibility of antiferromagnets \chi with the maximum at T \lsim |J_0|/D (J_0 is the Fourier component of the exchange interaction) and describes for the first time the singular behavior of \chi(H,T) at small temperatures and magnetic fields: \lim_{T\to 0}\lim_{H\to 0} \chi(H,T)=1/(2|J_0|)(1-1/D) and \lim_{H\to 0}\lim_{T\to 0} \chi(H,T)=1/(2|J_0|)

Thermodynamics of a mixed quantum-classical Heisenberg model in two dimensions

We study the planar antiferromagnetic Heisenberg model on a decorated hexagonal lattice, involving both classical spins (occupying the vertices) and quantum spins (occupying the middle of the links). This study is motivated by the description of a recently synthesized molecular magnetic compound. First, we trace out the spin 1/2 degrees of freedom to obtain a fully classical model with an effective ferromagnetic interaction. Then, using high temperature expansions and Monte Carlo simulations, we analyse its thermal and magnetic properties. We show that it provides a good quantitative description of the magnetic susceptibility of the molecular magnet in its paramagnetic phase.Comment: Revtex, 6 pages, 4 included postscript figures, fig.1 upon request to [email protected] . To appear in J. of Physic C (condensed matter

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

Fundamental measure theory for lattice fluids with hard core interactions

We present the extension of Rosenfeld's fundamental measure theory to lattice models by constructing a density functional for d-dimensional mixtures of parallel hard hypercubes on a simple hypercubic lattice. The one-dimensional case is exactly solvable and two cases must be distinguished: all the species with the same lebgth parity (additive mixture), and arbitrary length parity (nonadditive mixture). At the best of our knowledge, this is the first time that the latter case is considered. Based on the one-dimensional exact functional form, we propose the extension to higher dimensions by generalizing the zero-dimensional cavities method to lattice models. This assures the functional to have correct dimensional crossovers to any lower dimension, including the exact zero-dimensional limit. Some applications of the functional to particular systems are also shown.Comment: 22 pages, 7 figures, needs IOPP LaTeX styles file

Thermodynamic properties of ferromagnetic mixed-spin chain systems

Using a combination of high-temperature series expansion, exact diagonalization and quantum Monte Carlo, we perform a complementary analysis of the thermodynamic properties of quasi-one-dimensional mixed-spin systems with alternating magnetic moments. In addition to explicit series expansions for small spin quantum numbers, we present an expansion that allows a direct evaluation of the series coefficients as a function of spin quantum numbers. Due to the presence of excitations of both acoustic and optical nature, the specific heat of a mixed-spin chain displays a double-peak-like structure, which is more pronounced for ferromagnetic than for antiferromagnetic intra-chain exchange. We link these results to an analytically solvable half-classical limit. Finally, we extend our series expansion to incorporate the single-ion anisotropies relevant for the molecular mixed-spin ferromagnetic chain material MnNi(NO$_{2}$)$_{4}$(ethylenediamine)$_{2}$, with alternating spins of magnitude 5/2 and 1. Including a weak inter-chain coupling, we show that the observed susceptibility allows for an excellent fit, and the extraction of microscopic exchange parameters.Comment: 8 pages including 7 figures, submitted to Phys. Rev. B; series extended to 29th. QMC adde

Power-law correlations and orientational glass in random-field Heisenberg models

Monte Carlo simulations have been used to study a discretized Heisenberg ferromagnet (FM) in a random field on simple cubic lattices. The spin variable on each site is chosen from the twelve [110] directions. The random field has infinite strength and a random direction on a fraction x of the sites of the lattice, and is zero on the remaining sites. For x = 0 there are two phase transitions. At low temperatures there is a [110] FM phase, and at intermediate temperature there is a [111] FM phase. For x > 0 there is an intermediate phase between the paramagnet and the ferromagnet, which is characterized by a |k|^(-3) decay of two-spin correlations, but no true FM order. The [111] FM phase becomes unstable at a small value of x. At x = 1/8 the [110] FM phase has disappeared, but the power-law correlated phase survives.Comment: 8 pages, 12 Postscript figure

Double Exchange Alone Does Not Explain the Resistivity of La1−xSrxMnO3La_{1-x} Sr_x MnO_3

The $La_{1-x} Sr_x MnO_3$ system with $0.2 \lesssim x \lesssim 0.4$ has traditionally been modelled with a ``double exchange'' Hamiltonian, in which it is assumed that the only relevant physics is the tendency of carrier hopping to line up neighboring spins. We present a solution of the double exchange model, show it is incompatible with many aspects of the resistivity data, and propose that a strong electron-phonon interaction arising from a Jahn-Teller splitting of the outer Mn d-level plays a crucial role.Comment: Figure available via concentional mail. Contact [email protected]