Related papers: Natural Swarms in $\bf 3.99$ Dimensions
Anderson transition in three-dimensional systems is investigated using renormalization group theory. $\beta$-function of a very simple form is derived from a self-consistent consideration, and it gives a value $1+1/\sqrt{3}=1.58$ for the…
We consider a critical bisexual branching process in a random environment generated by independent and identically distributed random variables. Assuming that the process starts with a large number of pairs $N$, we prove that its extinction…
Interacting individuals in complex systems often give rise to coherent motion exhibiting coordinated global structures. Such phenomena are ubiquitously observed in nature, from cell migration, bacterial swarms, animal and insect groups, and…
Collective behaviour is a widespread phenomenon in biology, cutting through a huge span of scales, from cell colonies up to bird flocks and fish schools. The most prominent trait of collective behaviour is the emergence of global order:…
We study the scalar one-component two-dimensional (2D) $\phi^4$ model by computer simulations, with local Metropolis moves. The equilibrium exponents of this model are well-established, e.g. for the 2D $\phi^4$ model $\gamma= 1.75$ and…
This paper is devoted to a non-perturbative renormalization group (NPRG) analysis of Model A, which stands as a paradigm for the study of critical dynamics. The NPRG formalism has appeared as a valuable theoretical tool to investigate…
Following the Renormalization Group scheme recently developed by Pietronero {\it et al}, we introduce a simplifying strategy for the renormalization of the relaxation dynamics of sandpile models. In our scheme, five sub-cells at a generic…
New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and…
Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…
Sensory mechanisms in biology, from cells to humans, have the property of adaptivity, whereby the response produced by the sensor is adapted to the overall amplitude of the signal; reducing the sensitivity in the presence of strong…
The large N sigma model, in D<4 space-time dimensions, with disorder a function of d space dimensions, is analyzed via a renormalization group treatment. Critical exponents for average quantities are calculated, first to lowest order and…
In a recent preprint, ``A new universality class describes Vicsek's flocking phase in physical dimensions'', Patrick Jentsch and Chiu Fan Lee have computed the critical exponents of the Vicsek model in the ordered phase by means of…
This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (``updates''), followed…
Interaction strength is introduced in a model of evolution in d-dimension space. It is realized by imposing a constraint concerning 2d differences of fitnesses between that of any extremal site and those of its 2d nearest neighbours at each…
We analyse the critical behavior of two-dimensional N-vector spin systems with noncollinear order within the five-loop renormalization-group approximation. The structure of the RG flow is studied for different N leading to the conclusion…
Aggregation is a common behavior by which groups of organisms arrange into cohesive groups. Whether suspended in the air (like honey bee clusters), built on the ground (such as army ant bridges), or immersed in water (such as sludge worm…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
Critical behaviour of a nearly critical system, subjected to vivid turbulent mixing, is studied by means of the field theoretic renormalization group. Namely, relaxational stochastic dynamics of a non-conserved order parameter of the…
We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasi-statically changing the applied source at…
Techniques of `dynamic renormalization', developed earlier for undirected percolation and the contact model, are adapted to the setting of directed percolation, thereby obtaining solutions of several problems for directed percolation on…