Ground states and thermal states of the random field Ising model

The random field Ising model is studied numerically at both zero and positive temperature. Ground states are mapped out in a region of random and external field strength. Thermal states and thermodynamic properties are obtained for all temperatures using the the Wang-Landau algorithm. The specific heat and susceptibility typically display sharp peaks in the critical region for large systems and strong disorder. These sharp peaks result from large domains flipping. For a given realization of disorder, ground states and thermal states near the critical line are found to be strongly correlated--a concrete manifestation of the zero temperature fixed point scenario.Comment: 5 pages, 5 figures; new material added in this versio

Monte Carlo study of the two-dimensional site-diluted dipolar Ising model

By tempered Monte Carlo simulations, we study 2D site-diluted dipolar Ising systems. Dipoles are randomly placed on a fraction x of all L^2 sites in a square lattice, and point along a common crystalline axis. For x_c< x<=1, where x_c = 0.79(5), we find an antiferromagnetic phase below a temperature which vanishes as x approaches x_c from above. At lower values of x, we study (i) distributions of the spin--glass (SG) overlap q, (ii) their relative mean square deviation Delta_q^2 and kurtosis and (iii) xi_L/L, where xi_L is a SG correlation length. From their variation with temperature and system size, we find that the paramagnetic phase covers the entire T>0 range. Our results enable us to obtain an estimate of the critical exponent associated to the correlation length at T=0, 1/nu=0.35(10).Comment: 10 LaTeX pages, 10 figures, 1 table

Renormalization of modular invariant Coulomb gas and Sine-Gordon theories, and quantum Hall flow diagram

Using the renormalisation group (RG) we study two dimensional electromagnetic coulomb gas and extended Sine-Gordon theories invariant under the modular group SL(2,Z). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following proposal for a SL(2,Z) duality between different quantum Hall fluids, we discuss the analogy between this flow and the global quantum Hall phase diagram.Comment: 10 pages, 1 EPS figure include

Island Density in Homoepitaxial Growth:Improved Monte Carlo Results

We reexamine the density of two dimensional islands in the submonolayer regime of a homoepitaxially growing surface using the coarse grained Monte Carlo simulation with random sequential updating rather than parallel updating. It turns out that the power law dependence of the density of islands on the deposition rate agrees much better with the theoretical prediction than previous data obtained by other methods if random sequential instead of parallel updating is used.Comment: Latex with 2 PS figure file

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

Antiferromagnetic Quantum Spins on the Pyrochlore Lattice

The ground state of the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice is theoretically investigated. Starting from the limit of isolated tetrahedra, I include interactions between the tetrahedra and obtain an effective model for the spin-singlet ground state multiplet by third-order perturbation. I determine its ground state using the mean-field approximation and found a dimerized state with a four-sublattice structure, which agrees with the proposal by Harris et al. I also discuss chirality correlations and spin correlations for this state.Comment: 4 pages in 2-column format, 5 figures; To appear in J. Phys. Soc. Jpn. (Mar, 2001

Determination of step--edge barriers to interlayer transport from surface morphology during the initial stages of homoepitaxial growth

We use analytic formulae obtained from a simple model of crystal growth by molecular--beam epitaxy to determine step--edge barriers to interlayer transport. The method is based on information about the surface morphology at the onset of nucleation on top of first--layer islands in the submonolayer coverage regime of homoepitaxial growth. The formulae are tested using kinetic Monte Carlo simulations of a solid--on--solid model and applied to estimate step--edge barriers from scanning--tunneling microscopy data on initial stages of Fe(001), Pt(111), and Ag(111) homoepitaxy.Comment: 4 pages, a Postscript file, uuencoded and compressed. Physical Review B, Rapid Communications, in press

The Kagome Antiferromagnet with Defects: Satisfaction, Frustration, and Spin Folding in a Random Spin System

It is shown that site disorder induces noncoplanar states, competing with the thermal selection of coplanar states, in the nearest neighbor, classical kagome Heisenberg antiferromagnet (AFM). For weak disorder, it is found that the ground state energy is the sum of energies of separately satisfied triangles of spins. This implies that disorder does not induce conventional spin glass behavior. A transformation is presented, mapping ground state spin configurations onto a folded triangular sheet (a new kind of ``spin origami'') which has conformations similar to those of tethered membranes.Comment: REVTEX, 11 pages + 3 pictures upon reques

The Generic, Incommensurate Transition in the two-dimensional Boson Hubbard Model

The generic transition in the boson Hubbard model, occurring at an incommensurate chemical potential, is studied in the link-current representation using the recently developed directed geometrical worm algorithm. We find clear evidence for a multi-peak structure in the energy distribution for finite lattices, usually indicative of a first order phase transition. However, this multi-peak structure is shown to disappear in the thermodynamic limit revealing that the true phase transition is second order. These findings cast doubts over the conclusion drawn in a number of previous works considering the relevance of disorder at this transition.Comment: 13 pages, 10 figure