Functional renormalization group approach to the Yang-Lee edge singularity

We determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in $3 \leq d\leq 6$ Euclidean dimensions. We find very good agreement with high-temperature series data in $d = 3$ dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop $\epsilon = 6-d$ expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG $\beta$ functions is discussed and we estimate the error associated with $\mathcal{O}(\partial^4)$ truncations of the scale-dependent effective action.Comment: 10 pages, 4 figures, updated reference to supplementary materia

On spinodal points and Lee-Yang edge singularities

We address a number of outstanding questions associated with the analytic properties of the universal equation of state of the $\phi^4$ theory, which describes the critical behavior of the Ising model and ubiquitous critical points of the liquid-gas type. We focus on the relation between spinodal points that limit the domain of metastability for temperatures below the critical temperature, i.e., $T < T_{\rm c}$, and Lee-Yang edge singularities that restrict the domain of analyticity around the point of zero magnetic field $H$ for $T > T_{\rm c}$. The extended analyticity conjecture (due to Fonseca and Zamolodchikov) posits that, for $T < T_{\rm c}$, the Lee-Yang edge singularities are the closest singularities to the real $H$ axis. This has interesting implications, in particular, that the spinodal singularities must lie off the real $H$ axis for $d < 4$, in contrast to the commonly known result of the mean-field approximation. We find that the parametric representation of the Ising equation of state obtained in the $\varepsilon = 4-d$ expansion, as well as the equation of state of the ${\rm O}(N)$-symmetric $\phi^4$ theory at large $N$, are both nontrivially consistent with the conjecture. We analyze the reason for the difficulty of addressing this issue using the $\varepsilon$ expansion. It is related to the long-standing paradox associated with the fact that the vicinity of the Lee-Yang edge singularity is described by Fisher's $\phi^3$ theory, which remains nonperturbative even for $d\to 4$, where the equation of state of the $\phi^4$ theory is expected to approach the mean-field result. We resolve this paradox by deriving the Ginzburg criterion that determines the size of the region around the Lee-Yang edge singularity where mean-field theory no longer applies.Comment: 26 pages, 8 figures; v2: shortened Sec. 4.1 and streamlined arguments/notation in Sec. 4.2, details moved to appendix, added reference 1

From quantum to classical dynamics: The relativistic O(N)O(N) model in the framework of the real-time functional renormalization group

We investigate the transition from unitary to dissipative dynamics in the relativistic $O(N)$ vector model with the $\lambda (\varphi^{2})^{2}$ interaction using the nonperturbative functional renormalization group in the real-time formalism. In thermal equilibrium, the theory is characterized by two scales, the interaction range for coherent scattering of particles and the mean free path determined by the rate of incoherent collisions with excitations in the thermal medium. Their competition determines the renormalization group flow and the effective dynamics of the model. Here we quantify the dynamic properties of the model in terms of the scale-dependent dynamic critical exponent $z$ in the limit of large temperatures and in $2 \leq d \leq 4$ spatial dimensions. We contrast our results to the behavior expected at vanishing temperature and address the question of the appropriate dynamic universality class for the given microscopic theory.Comment: 32 pages, 12 captioned figures; revised and extended version accepted for publication in PR

Mycotoxin contamination of maize (Zea mays L.) samples in Hungary, 2012–2017

Mycotoxin contamination of maize often raises risks for human and animal health. The most frequently detected mycotoxins in maize are trichothecenes, fumonisins, and aflatoxin. A total number of 17,011 maize samples were tested by SGS for their mycotoxin content between 2012 and 2017. The toxin results clearly show that the southern areas of the country had higher levels of toxin contamination than the average. According to the dataset, aflatoxin contamination has become regular but the appearance of fumonisins was also more frequent. Deoxynivalenol toxin accumulation in crops can also reach dangerous levels under favorable ecological conditions. The fluctuation between years and regisons is decisively shaped by the weather conditions. However, the two pathogens with less virulence (Fusarium verticillioides and Aspergillus flavus) must be taken into account and the contribution of insect pests. 72.63% of the total fumonisin concentration was defined as fumonisin B1, 20.34% as fumonisin B2, and 7.03% as fumonisin B3. The correlations between the three fumonisins analogs were higly significant (P = 0.001), and correlation coefficient varied between 0.961 and 0.998 across the six years of evaluation. This is the first complex evaluation of deoxynivalenol, fumonisin, and aflatoxin contamination of maize samples in Hungary

First molecular phylogenetic insights into the evolution of Eriocaulon (Eriocaulaceae, Poales)

Eriocaulon is a genus of c. 470 aquatic and wetland species of the monocot plant family Eriocaulaceae. It is widely distributed in Africa, Asia and America, with centres of species richness in the tropics. Most species of Eriocaulon grow in wetlands although some inhabit shallow rivers and streams with an apparent adaptive morphology of elongated submerged stems. In a previous molecular phylogenetic hypothesis, Eriocaulon was recovered as sister of the African endemic genus Mesanthemum. Several regional infrageneric classifications have been proposed for Eriocaulon. This study aims to critically assess the existing infrageneric classifications through phylogenetic reconstruction of infrageneric relationships, based on DNA sequence data of four chloroplast markers and one nuclear marker. There is little congruence between our molecular results and previous morphology-based infrageneric classifications. However, some similarities can be found, including Fyson’s sect. Leucantherae and Zhang’s sect. Apoda. Further phylogenetic studies, particularly focusing on less well sampled regions such as the Neotropics, will help provide a more global overview of the relationships in Eriocaulon and may enable suggesting the first global infrageneric classification

Vegetation-based landscape regions of Hungary.

he first version of the map of the Hungarian vegetation-based landscape regions were prepared at the scale of 1 : 200,000 (1 km or higher resolution). The primary goal of the map was to provide an exact background for the presentation and evaluation of the data of theMÉTA database. Secondly, we intended to give an up-to-date and detailed vegetation-based division of Hungary with a comprehensive nomenclature of the regions. Regions were primarily defined on the basis of their present zonal vegetation, or their dominant extrazonal or edaphic vegetation. Where this was not possible, abiotic factors that influence the potential vegetation, the flora were taken into consideration, thus, political and economical factors were ignored. All region borders were defined by local expert botanists, mainly based on their field knowledge. The map differs in many features from the currently used, country- wide, flora- or geography-based divisions in many features. We consider our map to be temporary (i.e. a work map), and we plan to refine and improve it after 5 years of testing