Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram

We describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models. The density of states is modified at each step when the energy level is visited to produce a flat histogram. By carefully controlling the modification factor, we allow the density of states to converge to the true value very quickly, even for large systems. This algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability. In this paper, we apply our algorithm to both 1st and 2nd order phase transitions to demonstrate its efficiency and accuracy. We obtained direct simulational estimates for the density of states for two-dimensional ten-state Potts models on lattices up to $200 \times 200$ and Ising models on lattices up to $256 \times 256$. Applying this approach to a 3D $\pm J$ spin glass model we estimate the internal energy and entropy at zero temperature; and, using a two-dimensional random walk in energy and order-parameter space, we obtain the (rough) canonical distribution and energy landscape in order-parameter space. Preliminary data suggest that the glass transition temperature is about 1.2 and that better estimates can be obtained with more extensive application of the method.Comment: 22 pages (figures included

The use of Hediste diversicolor in the study of emerging contaminants

The contamination of aquatic environments has been the focus of research to understand effects on ecosystems and its species. Benthic organisms are considered potential targets since sediments act as sources and sinks for environmental contaminants. This review presents information on the effects of three types of emerging contaminants: pharmaceuticals (tested concentrations between 0.1 ng/L - 250 mg/L and 0.01 ng/g - 2.5 μg/g), metal-based nanoparticles (<100 nm) (tested concentrations between 10 μg/L - 1 mg/L and 5 - 140 μg/g) and micro(nano)plastics (tested concentrations between 5 μg/L - 50 mg/L and 10 - 50 mg/kg), on the polychaete Hediste diversicolor, a key species in estuarine/coastal ecosystems. Data shows that these contaminants promote alterations in burrowing activity (lowest concentration inducing effects: 10 ng/L), neurotransmission and damage related parameters (lowest concentration inducing effects: 100 ng/L). The characteristics of this polychaete, such as regenerative capacity, make the use of this species in biomedical studies involving environmental contaminants valuable.publishe