Long-range correlations and ensemble inequivalence in a generalized ABC model

A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For equal average densities of the three species, both dynamical models are demonstrated to exhibit detailed balance with respect to a Hamiltonian with long-range interactions. The model is found to exhibit two distinct phase diagrams, corresponding to the canonical (density-conserving) and grand canonical (density nonconserving) ensembles, as expected in long-range interacting systems. The implication of this result to nonequilibrium steady states, such as those of the ABC model with unequal average densities, are briefly discussed.Comment: 4 pages, 2 figures. v2: minor changes with an added reference, published versio

Of Ice Shields, Oceans, and Train Yards: Research-creation towards mythological contact with a feral terrain

This artistic research project is a speculative account that reflects on the artist-as-witness to the de-enchantments and re-enchantments of a feral terrain in post-industrial Montreal, Canada. Taking advantage of the confluence of this research and a renewal in the city's interest in the site, called the Falaise Saint-Jacques, the project calls into question the stark binaries that the idea of a separate "nature" implies. It builds on the work of art educators and academics who have resisted the siloing of art, focusing on the merging of public policy and place histories into an environmental art project. Content provided by implicated community members, the author's own experience, and scholarly and archival research coalesce into mythologies, articulated through visual arts. Artworks, used in this way, act as filters through which the viewer's understanding of geological scale may be shaped, translating the stories of millennia into decades, years, or moments. Finally, following from Indigenous Canadian knowledge, this research aims to model how mythologies that foreground connections to the land may offer a literal framework for seeing and relating to urban forms of nature. A field guide and zoetrope installations function as an analogue augmented reality machine that superimposes geological and mythological time onto the immediate present, literally and figuratively animating the landscape for the viewer, and creating a space for a mythological contact that introduces different, even opposing, conceptions of time to one another. Keywords: Research creation, Anthropocene, deep time, urban nature, environmental art, mythology, zoetrope, fieldwor

Molecular Hydrogen Formation on Low Temperature Surfaces in Temperature Programmed Desorption Experiments

The study of the formation of molecular hydrogen on low temperature surfaces is of interest both because it allows to explore elementary steps in the heterogeneous catalysis of a simple molecule and because of the applications in astrochemistry. Here we report results of experiments of molecular hydrogen formation on amorphous silicate surfaces using temperature-programmed desorption (TPD). In these experiments beams of H and D atoms are irradiated on the surface of an amorphous silicate sample. The desorption rate of HD molecules is monitored using a mass spectrometer during a subsequent TPD run. The results are analyzed using rate equations and the activation energies of the processes leading to molecular hydrogen formation are obtained from the TPD data. We show that a model based on a single isotope provides the correct results for the activation energies for diffusion and desorption of H atoms. These results can thus be used to evaluate the formation rate of H_2 on dust grains under the actual conditions present in interstellar clouds.Comment: 30 pages, 1 table, 6 figures. Published versio

Accurate rate coefficients for models of interstellar gas-grain chemistry

The methodology for modeling grain-surface chemistry has been greatly improved by taking into account the grain size and fluctuation effects. However, the reaction rate coefficients currently used in all practical models of gas-grain chemistry are inaccurate by a significant amount. We provide expressions for these crucial rate coefficients that are both accurate and easy to incorporate into gas-grain models. We use exact results obtained in earlier work, where the reaction rate coefficient was defined by a first-passage problem, which was solved using random walk theory. The approximate reaction rate coefficient presented here is easy to include in all models of interstellar gas-grain chemistry. In contrast to the commonly used expression, the results that it provides are in perfect agreement with detailed kinetic Monte Carlo simulations. We also show the rate coefficient for reactions involving multiple species.Comment: 4 pages, 2 figure

Phase fluctuations in the ABC model

We analyze the fluctuations of the steady state profiles in the modulated phase of the ABC model. For a system of $L$ sites, the steady state profiles move on a microscopic time scale of order $L^3$. The variance of their displacement is computed in terms of the macroscopic steady state profiles by using fluctuating hydrodynamics and large deviations. Our analytical prediction for this variance is confirmed by the results of numerical simulations

The grand canonical ABC model: a reflection asymmetric mean field Potts model

We investigate the phase diagram of a three-component system of particles on a one-dimensional filled lattice, or equivalently of a one-dimensional three-state Potts model, with reflection asymmetric mean field interactions. The three types of particles are designated as $A$, $B$, and $C$. The system is described by a grand canonical ensemble with temperature $T$ and chemical potentials $T\lambda_A$, $T\lambda_B$, and $T\lambda_C$. We find that for $\lambda_A=\lambda_B=\lambda_C$ the system undergoes a phase transition from a uniform density to a continuum of phases at a critical temperature $\hat T_c=(2\pi/\sqrt3)^{-1}$. For other values of the chemical potentials the system has a unique equilibrium state. As is the case for the canonical ensemble for this $ABC$ model, the grand canonical ensemble is the stationary measure satisfying detailed balance for a natural dynamics. We note that $\hat T_c=3T_c$, where $T_c$ is the critical temperature for a similar transition in the canonical ensemble at fixed equal densities $r_A=r_B=r_C=1/3$.Comment: 24 pages, 3 figure

Ensemble Inequivalence in the Spherical Spin Glass Model with Nonlinear Interactions

We investigate the ensemble inequivalence of the spherical spin glass model with nonlinear interactions of polynomial order $p$. This model is solved exactly for arbitrary $p$ and is shown to have first-order phase transitions between the paramagnetic and spin glass or ferromagnetic phases for $p \geq 5$. In the parameter region around the first-order transitions, the solutions give different results depending on the ensemble used for the analysis. In particular, we observe that the microcanonical specific heat can be negative and the phase may not be uniquely determined by the temperature.Comment: 15 pages, 10 figure

Ensemble Inequivalence and the Spin-Glass Transition

We report on the ensemble inequivalence in a many-body spin-glass model with integer spin. The spin-glass phase transition is of first order for certain values of the crystal field strength and is dependent whether it was derived in the microcanonical or the canonical ensemble. In the limit of infinitely many-body interactions, the model is the integer-spin equivalent of the random-energy model, and is solved exactly. We also derive the integer-spin equivalent of the de Almeida-Thouless line.Comment: 19 pages, 7 figure