Related papers: Comment on "A new universality class describes Vic…
We consider a Vicsek model of self-propelled particles with bounded confidence, where each particle interacts only with neighbors that have a similar direction. Depending on parameters, the system exhibits a continuous or discontinuous…
Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…
We review the theoretical description of the random field Ising and $O(N)$ models obtained from the functional renormalization group, either in its nonperturbative implementation or, in some limits, in perturbative implementations. The…
The perturbation theory expansion presented earlier to describe the phase-ordering kinetics in the case of a nonconserved scalar order parameter is generalized to the case of the $n$-vector model. At lowest order in this expansion, as in…
The Ising model is one of the most well known models in statistical physics, with its critical behavior governed by the Wilson-Fisher universality class (UC). When active motility is incorporated into the Ising model by, e.g., dictating…
Our community has a deep and sophisticated understanding of phase transitions and their universal scaling functions. We outline and advocate an ambitious program to use this understanding as an anchor for describing the surrounding phases.…
A new perturbation theory is proposed for studying finite-size effects near critical point of the $\phi^4$ model with a one-component order parameter. The new approach is based on the techniques of generating functional and functional…
In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of…
In flocking models, the collective motion of self-driven individuals leads to the formation of complex spatiotemporal patterns. The Standard Vicsek Model (SVM) considers individuals that tend to adopt the direction of movement of their…
We study second order phase transitions in non-conformal holographic models of gauge theory/string theory correspondence at finite temperature and zero chemical potential. We compute critical exponents of the bulk viscosity near the…
The percolation, Ising, and O($n$) models constitute fundamental systems in statistical and condensed matter physics. For short-range-interacting cases, the nature of their phase transitions is well established by renormalization-group…
Using the recent six loop renormalization group functions for Lee-Yang and percolation theory constructed by Schnetz from a scalar cubic Lagrangian, we deduce the $\epsilon$ expansion of the critical exponents for both cases. Estimates for…
Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…
In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential…
Vicsek Model is widely used in simulations of dry active matter. We re-examined two typical phase transitions in the original Vicsek model by using the velocity correlation length. One is the noise-driven disordered-to-ordered phase…
I formulate the theory of three dimensional "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- whose constituents all…
This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localisation and the Anderson model of localisation are…
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the…
It is well known that the 2D XY model exhibits an unusual infinite order phase transition belonging to the Kosterlitz-Thouless (KT) universality class. Introduction of a nematic coupling into the XY Hamiltonian leads to an additional phase…
We explain the recent numerical successes obtained by Tao Xiang's group, who developed and applied Tensor Renormalization Group methods for the Ising model on square and cubic lattices, by the fact that their new truncation method sharply…