Numerical study of the random field Ising model at zero and positive temperature

In this paper the three dimensional random field Ising model is studied at both zero temperature and positive temperature. Critical exponents are extracted at zero temperature by finite size scaling analysis of large discontinuities in the bond energy. The heat capacity exponent $\alpha$ is found to be near zero. The ground states are determined for a range of external field and disorder strength near the zero temperature critical point and the scaling of ground state tilings of the field-disorder plane is discussed. At positive temperature the specific heat and the susceptibility are obtained using the Wang-Landau algorithm. It is found that sharp peaks are present in these physical quantities for some realizations of systems sized $16^3$ and larger. These sharp peaks result from flipping large domains and correspond to large discontinuities in ground state bond energies. Finally, zero temperature and positive temperature spin configurations near the critical line are found to be highly correlated suggesting a strong version of the zero temperature fixed point hypothesis.Comment: 11 pages, 14 figure

Finite Temperature Dynamics of the Spin 1/2 Bond Alternating Heisenberg Antiferromagnetic Chain

We present results for the dynamic structure factor of the S=1/2 bond alternating Heisenberg chain over a large range of frequencies and temperatures. Data are obtained from a numerical evaluation of thermal averages based on the calculation of all eigenvalues and eigenfunctions for chains of up to 20 spins. Interpretation is guided by the exact temperature dependence in the noninteracting dimer limit which remains qualitatively valid up to an interdimer exchange $\lambda \approx 0.5$. The temperature induced central peak around zero frequency is clearly identified and aspects of the crossover to spin diffusion in its variation from low to high temperatures are discussed. The one-magnon peak acquires an asymmetric shape with increasing temperature. The two-magnon peak is dominated by the S=1 bound state which remains well defined up to temperatures of the order of J. The variation with temperature and wavevector of the integrated intensity for one and two magnon scattering and of the central peak are discussed.Comment: 8 pages, 8 figure

Quantum and Classical Spins on the Spatially Distorted Kagome Lattice: Applications to Volborthite

In Volborthite, spin-1/2 moments form a distorted Kagom\'e lattice, of corner sharing isosceles triangles with exchange constants $J$ on two bonds and $J'$ on the third bond. We study the properties of such spin systems, and show that despite the distortion, the lattice retains a great deal of frustration. Although sub-extensive, the classical ground state degeneracy remains very large, growing exponentially with the system perimeter. We consider degeneracy lifting by thermal and quantum fluctuations. To linear (spin wave) order, the degeneracy is found to stay intact. Two complementary approaches are therefore introduced, appropriate to low and high temperatures, which point to the same ordered pattern. In the low temperature limit, an effective chirality Hamiltonian is derived from non-linear spin waves which predicts a transition on increasing $J'/J$, from $\sqrt 3\times \sqrt 3$ type order to a new ferrimagnetic {\em striped chirality} order with a doubled unit cell. This is confirmed by a large-N approximation on the O($n$) model on this lattice. While the saddle point solution produces a line degeneracy, $O(1/n)$ corrections select the non-trivial wavevector of the striped chirality state. The quantum limit of spin 1/2 on this lattice is studied via exact small system diagonalization and compare well with experimental results at intermediate temperatures. We suggest that the very low temperature spin frozen state seen in NMR experiments may be related to the disconnected nature of classical ground states on this lattice, which leads to a prediction for NMR line shapes.Comment: revised, section V about exact diagonalization is extensively rewritten, 17 pages, 11 figures, RevTex 4, accepted by Phys. Rev.

Influence of lattice distortions in classical spin systems

We investigate a simple model of a frustrated classical spin chain coupled to adiabatic phonons under an external magnetic field. A thorough study of the magnetization properties is carried out both numerically and analytically. We show that already a moderate coupling with the lattice can stabilize a plateau at 1/3 of the saturation and discuss the deformation of the underlying lattice in this phase. We also study the transition to saturation where either a first or second order transition can occur, depending on the couplings strength.Comment: Submitted to Phys. Rev.

Effect of weak disorder in the Fully Frustrated XY model

The critical behaviour of the Fully Frustrated XY model in presence of weak positional disorder is studied in a square lattice by Monte Carlo methods. The critical exponent associated to the divergence of the chiral correlation length is found to be equal to 1.7 already at very small values of disorder. Furthermore the helicity modulus jump is found larger than the universal value expected in the XY model.Comment: 8 pages, 4 figures (revtex

Floating Phase in 1D Transverse ANNNI Model

To study the ground state of ANNNI chain under transverse field as a function of frustration parameter $\kappa$ and field strength $\Gamma$, we present here two different perturbative analyses. In one, we consider the (known) ground state at $\kappa=0.5$ and $\Gamma=0$ as the unperturbed state and treat an increase of the field from 0 to $\Gamma$ coupled with an increase of $\kappa$ from 0.5 to $0.5+r\Gamma$ as perturbation. The first order perturbation correction to eigenvalue can be calculated exactly and we could conclude that there are only two phase transition lines emanating from the point $\kappa=0.5$, $\Gamma=0$. In the second perturbation scheme, we consider the number of domains of length 1 as the perturbation and obtain the zero-th order eigenfunction for the perturbed ground state. From the longitudinal spin-spin correlation, we conclude that floating phase exists for small values of transverse field over the entire region intermediate between the ferromagnetic phase and antiphase.Comment: 11 pages, 11 figure

Finite size scaling in Villain's fully frustrated model and singular effects of plaquette disorder

The ground state and low T behavior of two-dimensional spin systems with discrete binary couplings are subtle but can be analyzed using exact computations of finite volume partition functions. We first apply this approach to Villain's fully frustrated model, unveiling an unexpected finite size scaling law. Then we show that the introduction of even a small amount of disorder on the plaquettes dramatically changes the scaling laws associated with the T=0 critical point.Comment: Latex with 3 ps figures. Last versio

A Spin Model for Investigating Chirality

Spin chirality has generated great interest recently both from possible applications to flux phases and intrinsically, as an example of a several-site magnetic order parameter that can be long-ranged even where simpler order parameters are not. Previous work (motivated by the flux phases) has focused on antiferromagnetic chiral order; we construct a model in which the chirality orders ferromagnetically and investigate the model's behavior as a function of spin. Enlisting the aid of exact diagonalization, spin-waves, perturbation theory, and mean fields, we conclude that the model likely has long-ranged chiral order for spins 1 and greater and no non-trivial chiral order for spin 1/2.Comment: uuencoded gzipped tarred plain tex fil

Spin Frustration and Orbital Order in Vanadium Spinels

We present the results of our theoretical study on the effects of geometrical frustration and the interplay between spin and orbital degrees of freedom in vanadium spinel oxides $A$V$_2$O$_4$ ($A$ = Zn, Mg or Cd). Introducing an effective spin-orbital-lattice coupled model in the strong correlation limit and performing Monte Carlo simulation for the model, we propose a reduced spin Hamiltonian in the orbital ordered phase to capture the stabilization mechanism of the antiferromagnetic order. Orbital order drastically reduces spin frustration by introducing spatial anisotropy in the spin exchange interactions, and the reduced spin model can be regarded as weakly-coupled one-dimensional antiferromagnetic chains. The critical exponent estimated by finite-size scaling analysis shows that the magnetic transition belongs to the three-dimensional Heisenberg universality class. Frustration remaining in the mean-field level is reduced by thermal fluctuations to stabilize a collinear ordering.Comment: 4 pages, 4 figures, proceedings submitted to SPQS200

Valence-bond crystal in a {111} slice of the pyrochlore antiferromagnet

We investigate theoretically the ordering effect of quantum spin fluctuations in a Heisenberg antiferromagnet on a two-dimensional network of corner sharing tetrahedra. This network is obtained as a {111} slice of the highly frustrated pyrochlore lattice, from which it inherits the equivalence of all three pairs of opposite bonds of each tetrahedron. The lowest-order (in 1/S) quantum corrections partially lift the huge degeneracy of the classical ground state and select an ensemble of states with long-range valence-bond order.Comment: 4 pages, 2 EPS figures. Minor revision: clarifications in response to referee comments, additional reference