Monte Carlo Study of the Anisotropic Heisenberg Antiferromagnet on the Triangular Lattice

We report a Monte Carlo study of the classical antiferromagnetic Heisenberg model with easy axis anisotropy on the triangular lattice. Both the free energy cost for long wavelength spin waves as well as for the formation of free vortices are obtained from the spin stiffness and vorticity modulus respectively. Evidence for two distinct Kosterlitz-Thouless types of defect-mediated phase transitions at finite temperatures is presented.Comment: 8 pages, 10 figure

Micromagnetic simulations of interacting dipoles on a fcc lattice: Application to nanoparticle assemblies

Micromagnetic simulations are used to examine the effects of cubic and axial anisotropy, magnetostatic interactions and temperature on M-H loops for a collection of magnetic dipoles on fcc and sc lattices. We employ a simple model of interacting dipoles that represent single-domain particles in an attempt to explain recent experimental data on ordered arrays of magnetoferritin nanoparticles that demonstrate the crucial role of interactions between particles in a fcc lattice. Significant agreement between the simulation and experimental results is achieved, and the impact of intra-particle degrees of freedom and surface effects on thermal fluctuations are investigated.Comment: 10 pages, 9 figure

GPU Concurrency: Weak Behaviours and Programming Assumptions

Concurrency is pervasive and perplexing, particularly on graphics processing units (GPUs). Current specifications of languages and hardware are inconclusive; thus programmers often rely on folklore assumptions when writing software. To remedy this state of affairs, we conducted a large empirical study of the concurrent behaviour of deployed GPUs. Armed with litmus tests (i.e. short concurrent programs), we questioned the assumptions in programming guides and vendor documentation about the guarantees provided by hardware. We developed a tool to generate thousands of litmus tests and run them under stressful workloads. We observed a litany of previously elusive weak behaviours, and exposed folklore beliefs about GPU programming---often supported by official tutorials---as false. As a way forward, we propose a model of Nvidia GPU hardware, which correctly models every behaviour witnessed in our experiments. The model is a variant of SPARC Relaxed Memory Order (RMO), structured following the GPU concurrency hierarchy

Monte Carlo Study of an Extended 3-State Potts Model on the Triangular Lattice

By introducing a chiral term into the Hamiltonian of the 3-state Potts model on a triangular lattice additional symmetries are achieved between the clockwise and anticlockwise states and the ferromagnetic state. This model is investigated using Monte Carlo methods. We investigate the full phase diagram and find evidence for a line tricritical points separating the ferromagnetic and antiferromagnetic phases.Comment: 6 pages, 10 figure

Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations

We have simulated the classical Heisenberg antiferromagnet on a triangular lattice using a local Monte Carlo algorithm. The behavior of the correlation length $\xi$, the susceptibility at the ordering wavevector $\chi(\bf Q)$, and the spin stiffness $\rho$ clearly reflects the existence of two temperature regimes -- a high temperature regime $T > T_{th}$, in which the disordering effect of vortices is dominant, and a low temperature regime $T < T_{th}$, where correlations are controlled by small amplitude spin fluctuations. As has previously been shown, in the last regime, the behavior of the above quantities agrees well with the predictions of a renormalization group treatment of the appropriate nonlinear sigma model. For $T > T_{th}$, a satisfactory fit of the data is achieved, if the temperature dependence of $\xi$ and $\chi(\bf Q)$ is assumed to be of the form predicted by the Kosterlitz--Thouless theory. Surprisingly, the crossover between the two regimes appears to happen in a very narrow temperature interval around $T_{th} \simeq 0.28$.Comment: 13 pages, 8 Postscript figure

Ising Spin Glass in a Transverse Magnetic Field

We study the three-dimensional quantum Ising spin glass in a transverse magnetic field following the evolution of the bond probability distribution under Renormalisation Group transformations. The phase diagram (critical temperature $T_c$ {\em vs} transverse field $\Gamma$) we obtain shows a finite slope near $T=0$, in contrast with the infinite slope for the pure case. Our results compare very well with the experimental data recently obtained for the dipolar Ising spin glass LiHo$_{0.167}$Y$_{0.833}$F$_4$, in a transverse field. This indicates that this system is more apropriately described by a model with short range interactions than by an equivalent Sherrington-Kirkpatrick model in a transverse field.Comment: 7 pages, RevTeX3, Nota Cientifica PUC-Rio 23/9

Evidence for the droplet/scaling picture of spin glasses

We have studied the Parisi overlap distribution for the three dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behaviour in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that sytem sizes larger than the correlation length have not been achieved.Comment: 4 pages, 6 figure

Periodic features in the Dynamic Structure Factor of the Quasiperiodic Period-doubling Lattice

We present an exact real-space renormalization group (RSRG) method for evaluating the dynamic structure factor of an infinite one-dimensional quasiperiodic period-doubling (PD) lattice. We observe that for every normal mode frequency of the chain, the dynamic structure factor $S(q,\omega)$ always exhibits periodicity with respect to the wave vector $q$ and the presence of such periodicity even in absence of translational invariance in the system is quite surprising. Our analysis shows that this periodicity in $S(q,\omega)$ actually indicates the presence of delocalized phonon modes in the PD chain. The Brillouin Zones of the lattice are found to have a hierarchical structure and the dispersion relation gives both the acoustic as well as optical branches. The phonon dispersion curves have a nested structure and we have shown that it is actually the superposition of the dispersion curves of an infinite set of periodic lattices.Comment: 9 pages, 3 postscript figures, REVTeX, To appear in Phys. Rev. B (1 February 1998-I

Multifractal Behaviour of n-Simplex Lattice

We study the asymptotic behaviour of resistance scaling and fluctuation of resistance that give rise to flicker noise in an {\em n}-simplex lattice. We propose a simple method to calculate the resistance scaling and give a closed-form formula to calculate the exponent, $\beta_L$, associated with resistance scaling, for any n. Using current cumulant method we calculate the exact noise exponent for n-simplex lattices.Comment: Latex, 9 pages including one figur