Phase Ordering Dynamics of ϕ4\phi^4 Theory with Hamiltonian Equations of Motion

Phase ordering dynamics of the (2+1)- and (3+1)-dimensional $\phi^4$ theory with Hamiltonian equations of motion is investigated numerically. Dynamic scaling is confirmed. The dynamic exponent $z$ is different from that of the Ising model with dynamics of model A, while the exponent $\lambda$ is the same.Comment: to appear in Int. J. Mod. Phys.

Topological origin of the phase transition in a mean-field model

We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory using the potential energy per particle V as a Morse function. The value of V where such a topological transition occurs equals the thermodynamic value of V at the phase transition and the number of (Morse) critical points grows very fast with the number of particles N. Furthermore, as in statistical mechanics, also in topology the way the thermodynamic limit is taken is crucial.Comment: REVTeX, 5 pages, with 1 eps figure included. Some changes in the text. To appear in Physical Review Letter

Anti-nationalist Europeans and pro-European nativists on the streets : visions of Europe from the left to the far right

For many left-wing and liberal social movement activists, support for ‘Europe’ and opposition to a ‘nationalist’ turn has become a key motivation for their activism. Paradoxically, however, their opponents at the other end of the political spectrum, far-right activists, also positively identify as European. This article analyses one of the key developments in the contemporary European protest arena, i.e. the dominance of European identities, even when activists strongly criticize real-existing European integration. First, we propose a novel conceptual framework that captures these dominant European identities. We distinguish between ‘anti-nationalist Europeans’ and ‘pro-European nativists’, underlining the existence of strong European identities across the political spectrum, deeply embedded in the mindset of activists even when they sharply criticize European integration in its current form. At the same time, these pro-European stances strongly differ in whether they are culturally inclusive or exclusive and how they relate to the question of nationalism or the nation state. Second, we apply these concepts to six key cases of movement mobilization in western Europe after the anti-austerity protests, shedding light on the anti-TTIP protests, Yanis Varoufakis’ DiEM25, the anti-Brexit movement in the UK, the Sardines in Italy (including their offshoot, the Herrings in Finland), the Identitarians and PEGIDA. Third, we further contextualize the ‘anti-nationalist Europeanism’ and ‘pro-European nativism’ of these six cases, emphasizing historical roots, the facilitation of coalition building, implications for transnational practices, and the meaning of silence. Methodologically, the article draws on online and offline publications, semi-structured interviews, and survey data

Topological aspects of geometrical signatures of phase transitions

Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the two-dimensional case, when a phase transition is present. The observed phenomenology strongly supports, though in an indirect way, a recently proposed topological conjecture about a topology change of the configuration space submanifolds as counterpart of a phase transition.Comment: REVTEX file, 4 pages, 5 figure

Topology and phase transitions: a paradigmatic evidence

We report upon the numerical computation of the Euler characteristic \chi (a topologic invariant) of the equipotential hypersurfaces \Sigma_v of the configuration space of the two-dimensional lattice $\phi^4$ model. The pattern \chi(\Sigma_v) vs. v (potential energy) reveals that a major topology change in the family {\Sigma_v}_{v\in R} is at the origin of the phase transition in the model considered. The direct evidence given here - of the relevance of topology for phase transitions - is obtained through a general method that can be applied to any other model.Comment: 4 pages, 4 figure

Comment on ``Deterministic equations of motion and phase ordering dynamics''

Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase ordering dynamics in the microcanonical $\phi^4$ model displays unusual scaling laws. We show here, performing more careful numerical investigations, that Zheng only observed transient dynamics mostly due to the corrections to scaling introduced by lattice effects, and that Ising-like (model A) phase ordering actually takes place at late times. Moreover, we argue that energy conservation manifests itself in different corrections to scaling.Comment: 5 pages, 4 figure

Land use influence on ambient PM2.5 and ammonia concentrations: Correlation analyses in the Lombardy region, Italy

Air pollution is identified as the primary environmental risk to health worldwide. Although most of the anthropic emissions are due to combustion processes, intensive farming activities may also contribute significantly, especially as a source of particulate matter 2.5 and ammonia. Investigations on particulate matter and precursors dynamics, identifying the most relevant environmental factors influencing their emissions, are critical to improving local and regional air quality policies. This work presents an analysis of the correlation between particulate matter 2.5 and ammonia concentrations, obtained from the Copernicus Atmosphere Monitoring Service, and local land use characteristics, to investigate the influence of agricultural activities on the space-time pollutant concentration patterns. The selected study area is the Lombardy region, northern Italy. Correlation is evaluated through Spearman’s coefficient. Agricultural areas resulted in a significant factor for high ammonia concentrations, while particulate matter 2.5 was strongly correlated with built-up areas. Natural areas resulted instead a protective factor for both pollutants. Results provide data-driven evidence of the land use effect on air quality, also quantifying such effects in terms of correlation coefficients magnitude

Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets

Based on the Hamiltonian equation of motion of the $\phi^4$ theory with quenched disorder, we investigate the depinning phase transition of the domain-wall motion in two-dimensional magnets. With the short-time dynamic approach, we numerically determine the transition field, and the static and dynamic critical exponents. The results show that the fundamental Hamiltonian equation of motion belongs to a universality class very different from those effective equations of motion.Comment: 6 pages, 7 figures, have been accept by EP

Hamiltonian dynamics of the two-dimensional lattice phi^4 model

The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics.Comment: REVTeX, 24 pages with 20 PostScript figure