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Given $d \in {\bf N}, \lambda >0$, the random connection model in a region $A \subseteq {\bf R}^d$ is a graph with vertex set given by a homogeneous Poisson point process of intensity $\lambda $ in $A$, with an edge placed between each pair…
Recently has been observed for some one-dimensional models that exhibit unexpected pseudo-transitions and quasi-phases. This pseudo-transition resembles a first- and second-order phase transition simultaneously. One of those models is the…
In the series of models with interacting particles in stochastic geometry, a new contribution presents the facet process which is defined in arbitrary Euclidean dimension. In 2D, 3D specially it is a process of interacting segments, flat…
Discrete Floquet time crystals (DFTC) are characterized by the spontaneous breaking of the discrete time-translational invariance characteristic of Floquet driven systems. In analogy with equilibrium critical points, also time-crystalline…
If a system undergoing phase transitions exhibits some characteristics of both first and second order, it is said to be of 'mixed order' or to display the Thouless effect. Such a transition is present in a simple model of a dynamic social…
We study a multi-type Ehrenfest process modeled as a finite quasi-birth-death (QBD) process. We assume that the transitions are allowed only to the two adjacent levels of the same phase and are characterized by linear rates. The crucial…
Using a simple analytic approach, we study the universal properties of second-order phase transition in holographic superconductor models. We explore a general model in arbitrary dimensions in which the condensation occurs via the…
We consider the set of points visited by the random walk on the discrete torus $(\mathbb{Z}/N\mathbb{Z})^d$, for $d \geq 3$, at times of order $uN^d$, for a parameter $u>0$ in the large-$N$ limit. We prove that the vacant set left by the…
Fluctuational transitions between two co-existing chaotic attractors, separated by a fractal basin boundary, are studied in a discrete dynamical system. It is shown that the mechanism for such transitions is determined by a hierarchy of…
We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the…
In this paper, we prove that Bernoulli percolation on bounded degree graphs with isoperimetric dimension $d>4$ undergoes a non-trivial phase transition (in the sense that $p_c<1$). As a corollary, we obtain that the critical point of…
The non-Hermitian extension of quasicrystals (QC) are highly tunable system for exploring novel material phases. While extended-localized phase transitions have been observed in one dimension, quantum phase transition in higher dimensions…
One-dimensional systems---ranging from travelling light to circuit cables and from DNA to superstrings---are ubiquitous and critically important to the human knowledge of the universe. However, our engagement with one-dimensional systems in…
We study a natural model of random 2-dimensional cubical complex which is a subcomplex of an n-dimensional cube, and where every possible square $2$-face is included independently with probability p. Our main result is to exhibit a sharp…
We develop a fluctuation theory of connectivities for subcritical random cluster models. The theory is based on a comprehensive nonperturbative probabilistic description of long connected clusters in terms of essentially one-dimensional…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
We introduce a new class of two-dimensional cellular automata with a bootstrap percolation-like dynamics. Each site can be either empty or occupied by a single particle and the dynamics follows a deterministic updating rule at discrete…
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of…
A liquid droplet is fragmented by a sudden pressurized-gas blow, and the resulting droplets, adhered to the window of a flatbed scanner, are counted and sized by computerized means. The use of a scanner plus image recognition software…
Adding quenched disorder to the one-dimensional asymmetric exclusion process is known to always induce phase separation. To test the robustness of this result, we introduce two modifications of the process that allow particles to bypass…