Related papers: Critical Dynamics of Self-Organizing Eulerian Walk…
We establish stable functional central limit theorems for scaled elephant random walks in the diffusive, critical, and superdiffusive cases using the martingale approach.
We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional…
The exact nature of the chiral phase transition in QCD is still under investigation. In $N_f=2$ and $N_f=(2+1)$ lattice simulations with staggered fermions the expected O($N$)-scaling behavior was observed. However, it is still not clear…
We study the scaling behaviour of the pseudo-critical couplings for the chiral phase transition in two-flavour QCD. We show that all existing results from lattice simulations on lattices with temporal extent $N_\tau = 4$, 6 and 8 can be…
We show that strongly-coupled, translation-invariant holographic IR phases at finite density can be classified according to the scaling behaviour of the metric, the electric potential and the electric flux introducing four critical…
We study the dynamics of a deterministic walk confined in a narrow two-dimensional space randomly filled with point-like targets. At each step, the walker visits the nearest target not previously visited. Complex dynamics is observed at…
We show that the Euler walk on a Cayley tree exhibits two regimes (dynamic phases): a condensed phase and a low-density phase. In the condensed phase the self-organized area grows as a compact domain. In the low-density phase the proportion…
The critical behavior of many physical systems involves two competing $n^{}_1-$ and $n^{}_2-$component order-parameters, ${\bf S}^{}_1$ and ${\bf S}^{}_2$, respectively, with $n=n^{}_1+n^{}_2$. Varying an external control parameter $g$,…
Lorentz lattice gases (LLGs) are discrete-time transport models in which a point particle moves ballistically between lattice sites and is scattered by randomly placed, quenched local scatterers such as ``rotators'' or ``mirrors.'' Despite…
This is a pedagogical review of the subject of linear polymers on deterministic finitely ramified fractals. For these, one can determine the critical properties exactly by real-space renormalization group technique. We show how this is used…
Numerically we simulate the short-time behaviour of the critical dynamics for the two dimensional Ising model and Potts model with an initial state of very high temperature and small magnetization. Critical initial increase of the…
Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by monte-carlo simulation near a critical point which marks a second-order phase transition from a active state to a effectively unique absorbing state.…
A class of Aubry-Andr\'e-Harper models of spin-orbit coupled electrons exhibits a topological phase diagram where two regions belonging to the same phase are split up by a multicritical point. The critical lines which meet at this point…
The dynamics of a one dimensional quantum walker on the lattice with two internal degrees of freedom, the coin states, is considered. The discrete time unitary dynamics is determined by the repeated action of a coin operator in U(2) on the…
This work analyzes fractional continuous-time random walks on two-layer multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson distribution of a walker to become active, while a jump to one of its neighbors depends…
Nonequilibrium phase transitions are characterized by the so-called critical exponents, each of which is related to a different observable. Systems that share the same set of values for these exponents also share the same universality…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
The analysis of the radial distribution function of a system provides a possible procedure for uncovering interaction rules between individuals out of collective movement patterns. This approach from classical statistical mechanics has…
Disordered non-interacting systems are classified into ten symmetry classes, with the unitary class being the most fundamental. The three and four dimensional unitary universality classes are attracting renewed interest because of their…
In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…