Related papers: Statistical description of domains in the Potts mo…
We present numerical investigations of the short-time dynamics at criticality in the 1D Potts model with power-law decaying interactions of the form 1/r^{1+sigma}. The scaling properties of the magnetization, autocorrelation function and…
We show that the dynamics of simple disordered models, like the directed Trap Model and the Random Energy Model, takes place at a coexistence point between active and inactive dynamical phases. We relate the presence of a dynamic phase…
We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not…
LHC ALICE data are interpreted in terms of statistical power-law tailed pT spectra. As explanation we derive such statistical distributions for particular particle number fluctuation patterns in a finite heat bath exactly, and for general…
The Potts model with invisible states was introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where $Z_q$ symmetry is spontaneously broken. It differs from…
We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark that Zipf's law is a consequence of a power law fragment size distribution with exponent $\tau \simeq 2$. We also recall why the presence of such distribution is…
It is shown that power law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium which are expected to occur in collisionless plasmas containing fully developed quasi-stationary turbulence.…
In this paper, we consider the relationship between phase-type distributions and positive systems through practical examples. Phase-type distributions, commonly used in modelling dynamic systems, represent the temporal evolution of a set of…
Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that…
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…
Using numerical simulations, we investigate the distribution of Kondo temperatures at the Anderson transition. In agreement with previous work, we find that the distribution has a long tail at small Kondo temperatures. Recently, an…
We review the ubiquitous presence in multiparticle production processes of quasi-power law distributions (i.e., distributions following pure power laws for large values of the argument but remaining finite, usually exponential, for small…
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two…
We study a generalization of the one-dimensional disordered Potts model, which exhibits glassy properties at low temperature. The real space properties of inherent structures visited dynamically are analyzed through a decomposition into…
The three-state Potts model is numerically investigated on three-dimensional simple cubic lattices of up to \(128^3\) volume, concentrating on the neighborhood of the first-order phase transition separating the ordered and disordered…
Zipf's law is well known in linguistics: the frequency of a word is inversely proportional to its rank. This is a special case of a more general power law, a common phenomenon in many kinds of real-world statistical data. Here, it is shown…
Since its introduction, the Potts model has gained widespread popularity across various fields due to its diverse applications. Even minor advancements in this model continue to captivate scientists worldwide, and small modifications often…
Using an infinite Matrix Product State (iMPS) technique based on the time-dependent variational principle (TDVP), we study two major types of dynamical phase transitions (DPT) in the one-dimensional transverse-field Ising model (TFIM) with…
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines - from astronomy to demographics to software structure to economics to linguistics to zoology, and even…
We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free…