Related papers: Zipf's law and phase transition
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…
We examine the order of the phase transition in the Potts model by using the graph representation for the partition function, which allows treating a non-integer number of Potts states. The order of transition is determined by the analysis…
The Fortuin-Kasteleyn (FK) random cluster model, which can be exactly mapped from the $q$-state Potts spin model, is a correlated bond percolation model. By extensive Monte Carlo simulations, we study the FK bond representation of the…
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…
We consider discrete-time switching systems composed of a finite family of affine sub-dynamics. First, we recall existing results and present further analysis on the stability problem, the existence and characterization of compact…
An order--disorder phase transition is observed for Ising-like systems even for arbitrarily chosen probabilities of spins flips [K. Malarz et al, Int. J. Mod. Phys. C 22, 719 (2011)]. For such athermal dynamics one must define $(z+1)$ spin…
The formation of sentences is a highly structured and history-dependent process. The probability of using a specific word in a sentence strongly depends on the 'history' of word-usage earlier in that sentence. We study a simple…
The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the systems behavior. In addition, empirical data typically…
Distinguishing different topologically ordered phases and characterizing phase transitions between them is a difficult task due to the absence of local order parameters. In this paper, we use a combination of analytical and numerical…
A cluster algorithm is presented for the simulation of the q-state Potts models in which the number of spins is conserved in each state. The algorithm constructs Fortuin-Kasteleyn cluster configurations from spin configurations, in a way…
Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a…
The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of…
Nonreciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit and the critical behavior of the…
We study geometrical properties of interfaces in the random-temperature q-states Potts model as an example of a conformal field theory weakly perturbed by quenched disorder. Using conformal perturbation theory in q-2 we compute the fractal…
An Ising model with local Glauber dynamics is studied under the influence of additional kinetic restrictions for the spin-flip rates depending on the orientation of neighboring spins. Even when the static interaction between the spins is…
A model of phase transitions with coupling between the order parameter and its gradient is proposed. It is shown, that this nonlinear model is suitable for the description of phase transitions accompanied by the formation of spatially…
The length of coding sequence series in microbial genomes were regarded as a fluctuating system and characterized by the methods of statistical physics. The distribution and the correlatin properties of 50 genomes including bacteria and…
We investigate numerically the dynamics of traveling clusters in systems of phase oscillators, some of which possess positive couplings and others negative couplings. The phase distribution, speed of traveling, and average separation…
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Based on the idea from general fractals and scaling,…
In this paper we investigate peculiarities of phase transition high-symmetry - incommensurate phase in inhomogeneous systems. We obtain the nonlinear dispersion law and then present a renormalization group analysis of phase transitions in…