Related papers: Sharp phase transition for the random-cluster and …
In a seminal paper, Weitz showed that for two-state spin systems, such as the Ising and hardcore models from statistical physics, correlation decay on trees implies correlation decay on arbitrary graphs. The key gadget in Weitz's reduction…
We study the survival/extinction phase transition for contact processes with quenched disorder. The disorder is given by a locally finite random graph with vertices indexed by the integers that is assumed to be invariant under index shifts…
The influence of uncorrelated, quenched disorder on the phase transition of two dimensional Potts models will be reviewed. After an introduction where the conditions of relevance of quenched randomness on phase transitions are exemplified…
Recent experiments and simulations of amorphous solids plastically deformed by oscillatory drive have foundsurprising behavior - for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity…
Machine learning-inspired techniques have emerged as a new paradigm for analysis of phase transitions in quantum matter. In this work, we introduce a supervised learning algorithm for studying critical phenomena from measurement data, which…
The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of…
For a family of random-cluster models with cluster weights $q\geq 1$, we prove that the probability that $0$ is connected to $x$ is asymptotically equal to $\tfrac{1}{q}\chi(\beta)^{2}\beta J_{0,x}$. The method developed in this article can…
We consider the level-sets of continuous Gaussian fields on $\mathbb{R}^d$ above a certain level $-\ell\in \mathbb{R}$, which defines a percolation model as $\ell$ varies. We assume that the covariance kernel satisfies certain regularity,…
The phase transition in the q-state Potts model with homogeneous ferromagnetic couplings is strongly first order for large q, while is rounded in the presence of quenched disorder. Here we study this phenomenon on different two-dimensional…
We study a $q$-state Potts model on the square grid when $q>4$ at the point $T_c(q)$ of its (discontinous) transition. This model exhibits exactly $q+1$ extremal Gibbs measures: $q$ ordered (monochromatic) and one disordered (free). The…
It is proposed that the $O(n)$ spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
The phase transitions of random-field q-state Potts models in d=3 dimensions are studied by renormalization-group theory by exact solution of a hierarchical lattice and, equivalently, approximate Migdal-Kadanoff solutions of a cubic…
We consider the Random-Cluster model on $\mathbb{Z}^d$ with interactions of infinite range of the form $J_x = \psi(x)\mathsf{e}^{-\rho(x)}$ with $\rho$ a norm on $\mathbb{Z}^d$ and $\psi$ a subexponential correction. We first provide an…
We perform extensive Monte Carlo simulations of the 10-state Potts model on quenched two-dimensional $\Phi^3$ gravity graphs to study the effect of quenched coordination number randomness on the nature of the phase transition, which is…
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…
The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters size distributions is developed. It allows for full description of percolation transition…
The numerical simulation of strongly first-order phase transitions has remained a notoriously difficult problem even for classical systems due to the exponentially suppressed (thermal) equilibration in the vicinity of such a transition. In…
A Monte Carlo algorithm is proposed to simulate ferromagnetic q-state Potts model for any real q>0. A single update is a random sequence of disordering and deterministic moves, one for each link of the lattice. A disordering move attributes…
The two-dimensional q-state Potts model is subjected to a Z_q symmetric disorder that allows for the existence of a Nishimori line. At q=2, this model coincides with the +/- J random-bond Ising model. For q>2, apart from the usual pure and…