Dynamical Probability Distribution Function of the SK Model at High Temperatures

The microscopic probability distribution function of the Sherrington-Kirkpatrick (SK) model of spin glasses is calculated explicitly as a function of time by a high-temperature expansion. The resulting formula to the third order of the inverse temperature shows that an assumption made by Coolen, Laughton and Sherrington in their recent theory of dynamics is violated. Deviations of their theory from exact results are estimated quantitatively. Our formula also yields explicit expressions of the time dependence of various macroscopic physical quantities when the temperature is suddenly changed within the high-temperature region.Comment: LaTeX, 6 pages, Figures upon request (here revised), To be published in J. Phys. Soc. Jpn. 65 (1996) No.

Confinement Effects in Antiferromagnets

Phase equilibrium in confined Ising antiferromagnets was studied as a function of the coupling (v) and a magnetic field (h) at the surfaces, in the presence of an external field H. The ground state properties were calculated exactly for symmetric boundary conditions and nearest-neighbor interactions, and a full zero-temperature phase diagram in the plane v-h was obtained for films with symmetry-preserving surface orientations. The ground-state analysis was extended to the H-T plane using a cluster-variation free energy. The study of the finite-T properties (as a function of v and h) reveals the close interdependence between the surface and finite-size effects and, together with the ground-state phase diagram, provides an integral picture of the confinement in anisotropic antiferromagnets with surfaces that preserve the symmetry of the order parameter.Comment: 10 pages, 8 figures, Accepted in Phys. Rev.

Longitudinal magnetic excitations in classical spin systems

Using spin dynamics simulations we predict the splitting of the longitudinal spin wave peak in all antiferromagnets with single site anisotropy into two peaks separated by twice the energy gap at the Brillouin zone center. This phenomenon has yet to be observed experimentally but can be easily investigated through neutron scattering experiments on MnF$_2$ and FeF$_2$. We have also determined that for all classical Heisenberg models the longitudinal propagative excitations are entirely multiple spin-wave in nature.Comment: four pages three figures, the last two postscript files are two parts of the third figur

The lifespan method as a tool to study criticality in absorbing-state phase transitions

In a recent work, a new numerical method (the lifespan method) has been introduced to study the critical properties of epidemic processes on complex networks [Phys. Rev. Lett. \textbf{111}, 068701 (2013)]. Here, we present a detailed analysis of the viability of this method for the study of the critical properties of generic absorbing-state phase transitions in lattices. Focusing on the well understood case of the contact process, we develop a finite-size scaling theory to measure the critical point and its associated critical exponents. We show the validity of the method by studying numerically the contact process on a one-dimensional lattice and comparing the findings of the lifespan method with the standard quasi-stationary method. We find that the lifespan method gives results that are perfectly compatible with those of quasi-stationary simulations and with analytical results. Our observations confirm that the lifespan method is a fully legitimate tool for the study of the critical properties of absorbing phase transitions in regular lattices

Tunability of Critical Casimir Interactions by Boundary Conditions

We experimentally demonstrate that critical Casimir forces in colloidal systems can be continuously tuned by the choice of boundary conditions. The interaction potential of a colloidal particle in a mixture of water and 2,6-lutidine has been measured above a substrate with a gradient in its preferential adsorption properties for the mixture's components. We find that the interaction potentials at constant temperature but different positions relative to the gradient continuously change from attraction to repulsion. This demonstrates that critical Casimir forces respond not only to minute temperature changes but also to small changes in the surface properties.Comment: 4 figures; http://www.iop.org/EJ/article/0295-5075/88/2/26001/epl_88_2_26001.htm

Measuring the equation of state of a hard-disc fluid

We use video microscopy to study a two-dimensional (2D) model fluid of charged colloidal particles suspended in water and compute the pressure from the measured particle configurations. Direct experimental control over the particle density by means of optical tweezers allows the precise measurement of pressure as a function of density. We compare our data with theoretical predictions for the equation of state, the pair-correlation function and the compressibility of a hard-disc fluid and find good agreement, both for the fluid and the solid phase. In particular the location of the transition point agrees well with results from Monte Carlo simulations.Comment: 7 pages, to appear in EPL, slightly corrected versio

Some Finite Size Effects in Simulations of Glass Dynamics

We present the results of a molecular dynamics computer simulation in which we investigate the dynamics of silica. By considering different system sizes, we show that in simulations of the dynamics of this strong glass former surprisingly large finite size effects are present. In particular we demonstrate that the relaxation times of the incoherent intermediate scattering function and the time dependence of the mean squared displacement are affected by such finite size effects. By compressing the system to high densities, we transform it to a fragile glass former and find that for that system these types of finite size effects are much weaker.Comment: 12 pages of RevTex, 4 postscript figures available from W. Ko

Properties of Interfaces in the two and three dimensional Ising Model

To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the $2D$ and $3D$ Ising model. Following Binder we extract the interfacial free energy from the infinite volume limit of the magnetic probability density. Stringent tests of the numerical methods are performed by reproducing with high precision exact $2D$ results. In the physically more interesting $3D$ case we estimate the amplitude $F^s_0$ of the critical interfacial tension $F^s = F^s_0 t^\mu$ to be $F^s_0 = 1.52 \pm 0.05$. This result is in good agreement with a previous MC calculation by Mon, as well as with experimental results for related amplitude ratios. In addition, we study in some details the shape of the magnetic probability density for temperatures below the Curie point.Comment: 25 pages; sorry no figures include

Surface critical exponents at a uniaxial Lifshitz point

Using Monte Carlo techniques, the surface critical behaviour of three-dimensional semi-infinite ANNNI models with different surface orientations with respect to the axis of competing interactions is investigated. Special attention is thereby paid to the surface criticality at the bulk uniaxial Lifshitz point encountered in this model. The presented Monte Carlo results show that the mean-field description of semi-infinite ANNNI models is qualitatively correct. Lifshitz point surface critical exponents at the ordinary transition are found to depend on the surface orientation. At the special transition point, however, no clear dependency of the critical exponents on the surface orientation is revealed. The values of the surface critical exponents presented in this study are the first estimates available beyond mean-field theory.Comment: 10 pages, 7 figures include

Critical Exponents of the Classical 3D Heisenberg Model: A Single-Cluster Monte Carlo Study

We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors. In one set of simulations we employ the usual finite-size scaling methods to compute the critical exponents $\nu,\alpha,\beta,\gamma, \eta$ from a few measurements in the vicinity of the critical point, making extensive use of histogram reweighting and optimization techniques. In another set of simulations we report measurements of improved estimators for the spatial correlation length and the susceptibility in the high-temperature phase, obtained on lattices with up to $100^3$ spins. This enables us to compute independent estimates of $\nu$ and $\gamma$ from power-law fits of their critical divergencies.Comment: 33 pages, 12 figures (not included, available on request). Preprint FUB-HEP 19/92, HLRZ 77/92, September 199