Connecting the vulcanization transition to percolation

The vulcanization transition is addressed via a minimal replica-field-theoretic model. The appropriate long-wave-length behavior of the two- and three-point vertex functions is considered diagrammatically, to all orders in perturbation theory, and identified with the corresponding quantities in the Houghton-Reeve-Wallace field-theoretic approach to the percolation critical phenomenon. Hence, it is shown that percolation theory correctly captures the critical phenomenology of the vulcanization transition associated with the liquid and critical states.Comment: 9 pages, 5 figure

Hierarchic trees with branching number close to one: noiseless KPZ equation with additional linear term for imitation of 2-d and 3-d phase transitions.

An imitation of 2d field theory is formulated by means of a model on the hierarhic tree (with branching number close to one) with the same potential and the free correlators identical to 2d correlators ones. Such a model carries on some features of the original model for certain scale invariant theories. For the case of 2d conformal models it is possible to derive exact results. The renormalization group equation for the free energy is noiseless KPZ equation with additional linear term.Comment: latex, 5 page

Diffusive transport and self-consistent dynamics in coupled maps

The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps. Self-consistency, i.e. the back-influence of the transported quantity on the velocity field of the driving flow, despite of its critical importance, is usually overlooked in the description of realistic systems, for example in plasma physics. We propose a class of self-consistent models consisting of an ensemble of maps globally coupled through a mean field. Depending on the kind of coupling, two different general types of self-consistent maps are considered: maps coupled to the field only through the phase, and fully coupled maps, i.e. through the phase and the amplitude of the external field. The analogies and differences of the diffusion properties of these two kinds of maps are discussed in detail.Comment: 13 pages, 14 figure

Coral Symbiodinium Community Composition Across the Belize Mesoamerican Barrier Reef System is Influenced by Host Species and Thermal Variability

Reef-building corals maintain a symbiotic relationship with dinoflagellate algae of the genus Symbiodinium, and this symbiosis is vital for the survival of the coral holobiont. Symbiodinium community composition within the coral host has been shown to influence a coral’s ability to resist and recover from stress. A multitude of stressors including ocean warming, ocean acidification, and eutrophication have been linked to global scale decline in coral health and cover in recent decades. Three distinct thermal regimes (highTP, modTP, and lowTP) following an inshore-offshore gradient of declining average temperatures and thermal variation were identified on the Belize Mesoamerican Barrier Reef System (MBRS). Quantitative metabarcoding of the ITS-2 locus was employed to investigate differences and similarities in Symbiodinium genetic diversity of the Caribbean corals Siderastrea siderea, S. radians, and Pseudodiploria strigosa between the three thermal regimes. A total of ten Symbiodinium lineages were identified across the three coral host species. S. siderea was associated with distinct Symbiodinium communities; however, Symbiodinium communities of its congener, S. radians and P. strigosa, were more similar to one another. Thermal regime played a role in defining Symbiodinium communities in S. siderea but not S. radians or P. strigosa. Against expectations, Symbiodinium trenchii, a symbiont known to confer thermal tolerance, was dominant only in S. siderea at one sampled offshore site and was rare inshore, suggesting that coral thermal tolerance in more thermally variable inshore habitats is achieved through alternative mechanisms. Overall, thermal parameters alone were likely not the only primary drivers of Symbiodinium community composition, suggesting that environmental variables unrelated to temperature (i.e., light availability or nutrients) may play key roles in structuring coral-algal communities in Belize and that the relative importance of these environmental variables may vary by coral host species

Statistical mechanics of permanent random atomic and molecular networks: Structure and heterogeneity of the amorphous solid state

Under sufficient permanent random covalent bonding, a fluid of atoms or small molecules is transformed into an amorphous solid network. Being amorphous, local structural properties in such networks vary across the sample. A natural order parameter, resulting from a statistical-mechanical approach, captures information concerning this heterogeneity via a certain joint probability distribution. This joint probability distribution describes the variations in the positional and orientational localization of the particles, reflecting the random environments experienced by them, as well as further information characterizing the thermal motion of particles. A complete solution, valid in the vicinity of the amorphous solidification transition, is constructed essentially analytically for the amorphous solid order parameter, in the context of the random network model and approach introduced by Goldbart and Zippelius [Europhys. Lett. 27, 599 (1994)]. Knowledge of this order parameter allows us to draw certain conclusions about the stucture and heterogeneity of randomly covalently bonded atomic or molecular network solids in the vicinity of the amorphous solidification transition. Inter alia, the positional aspects of particle localization are established to have precisely the structure obtained perviously in the context of vulcanized media, and results are found for the analogue of the spin glass order parameter describing the orientational freezing of the bonds between particles.Comment: 31 pages, 5 figure

Numerical Replica Limit for the Density Correlation of the Random Dirac Fermion

The zero mode wave function of a massless Dirac fermion in the presence of a random gauge field is studied. The density correlation function is calculated numerically and found to exhibit power law in the weak randomness with the disorder dependent exponent. It deviates from the power law and the disorder dependence becomes frozen in the strong randomness. A classical statistical system is employed through the replica trick to interpret the results and the direct evaluation of the replica limit is demonstrated numerically. The analytic expression of the correlation function and the free energy are also discussed with the replica symmetry breaking and the Liouville field theory.Comment: 5 pages, 4 figures, REVTe

Temperature Dependence of Hall Response in Doped Antiferromagnets

Using finite-temperature Lanczos method the frequency-dependent Hall response is calculated numerically for the t-J model on the square lattice and on ladders. At low doping, both the high-frequency RH* and the d.c. Hall coefficient RH0 follow qualitatively similar behavior at higher temperatures: being hole-like for T > Ts~1.5J and weakly electron-like for T < Ts. Consistent with experiments on cuprates, RH0 changes, in contrast to RH*, again to the hole-like sign below the pseudogap temperature T*, revealing a strong temperature variation for T->0.Comment: LaTeX, 4 pages, 4 figures, submitted to PR

Critical generalized inverse participation ratio distributions

The system size dependence of the fluctuations in generalized inverse participation ratios (IPR's) $I_{\alpha}(q)$ at criticality is investigated numerically. The variances of the IPR logarithms are found to be scale-invariant at the macroscopic limit. The finite size corrections to the variances decay algebraically with nontrivial exponents, which depend on the Hamiltonian symmetry and the dimensionality. The large-$q$ dependence of the asymptotic values of the variances behaves as $q^2$ according to theoretical estimates. These results ensure the self-averaging of the corresponding generalized dimensions.Comment: RevTex4, 5 pages, 4 .eps figures, to be published in Phys. Rev.

Eukaryotic plankton communities across reef environments in Bocas del Toro Archipelago, Panamá

Variation in light and temperature can influence the genetic diversity and structure of marine plankton communities. While open-ocean plankton communities receive much scientific attention, little is known about how environmental variation affects plankton communities on tropical coral reefs. Here, we characterize eukaryotic plankton communities on coral reefs across the Bocas del Toro Archipelago, Panamá. Temperature loggers were deployed, and midday light levels were measured to quantify environmental differences across reefs at four inshore and four offshore sites (Inshore = Punta Donato, Smithsonian Tropical Research Institute (STRI) Point, Cristobal, Punta Laurel and Offshore = Drago Mar, Bastimentos North, Bastimentos South, and Cayo de Agua). Triplicate vertical plankton tows were collected midday, and high-throughput 18S ribosomal DNA metabarcoding was leveraged to investigate the relationship between eukaryotic plankton community structure and inshore/offshore reef environments. Plankton communities from STRI Point were additionally characterized in the morning (~ 08:00), midday (~ 12:00), and late-day (~ 16:00) to quantify temporal variation within a single site. We found that inshore reefs experienced higher average seawater temperatures, while offshore sites offered higher light levels, presumably associated with reduced water turbidity on reefs further from shore. These significant environmental differences between inshore and offshore reefs corresponded with overall plankton community differences. We also found that temporal variation played a structuring role within these plankton communities, and conclude that time of community sampling is an important consideration for future studies. Follow-up studies focusing on more intensive sampling efforts across space and time, coupled with techniques that can detect more subtle genetic differences between and within communities will more fully capture plankton dynamics in this region and beyond

Aging dynamics of heterogeneous spin models

We investigate numerically the dynamics of three different spin models in the aging regime. Each of these models is meant to be representative of a distinct class of aging behavior: coarsening systems, discontinuous spin glasses, and continuous spin glasses. In order to study dynamic heterogeneities induced by quenched disorder, we consider single-spin observables for a given disorder realization. In some simple cases we are able to provide analytical predictions for single-spin response and correlation functions. The results strongly depend upon the model considered. It turns out that, by comparing the slow evolution of a few different degrees of freedom, one can distinguish between different dynamic classes. As a conclusion we present the general properties which can be induced from our results, and discuss their relation with thermometric arguments.Comment: 39 pages, 36 figure