Related papers: Cluster Percolation and First Order Phase Transiti…
We have simulated, by using cluster algorithm, the $q=8$ state Potts model in two-dimension with varying amount of quenched bond randomness. We have shown that there exist a finite size dependent threshold value of the introduced quenched…
We prove sharpness of the phase transition for the random-cluster model with $q \geq 1$ on graphs of the form $\mathcal{S} := \mathcal{G} \times S$, where $\mathcal{G}$ is a planar lattice with mild symmetry assumptions, and $S$ a finite…
We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their…
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…
Using the group structure of the state space of $q-$state models, a new definition of contour for long-range spin-systems in $\Z^d$ ($d\geq 2$), and a multidimensional version of Fr\"{o}hlich-Spencer contours, we prove phase transition for…
At the critical point in two dimensions, the number of percolation clusters of enclosed area greater than A is proportional to 1/A, with a proportionality constant C that is universal. We show theoretically (based upon Coulomb gas methods),…
We prove phase transition for the non-symmetric continuum Potts model with background interaction, by generalizing the methods introduced in the symmetric case by Georgii and H\"aggstr\"om. The proof relies on a Fortuin-Kasteleyn…
The description of thermodynamic phase transitions in terms of percolation transitions of suitably defined clusters has a long tradition and boasts a number of important successes, the most prominent ones being in ferromagnetic lattice…
The study of the phase transition in planar FK-percolation on the square lattice has seen significant recent breakthroughs. The model undergoes a change in the nature of its phase transition at $q = 4$, transitioning from a continuous to a…
We study the phase diagram of the three-state Potts model on a triangular lattice with general interactions (ferro/antiferromagnetic) between nearest neighbor spins. When the interactions along two lattice-vector directions are…
We perform Monte Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are…
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…
The stability of the topological order phase induced by the $Z_3$ Kitaev model, which is a candidate for fault-tolerant quantum computation, against the local order phase induced by the 3-State Potts model is studied. We show that the low…
The compact Abelian Higgs model is simulated on a cubic lattice where it possesses vortex lines and pointlike magnetic monopoles as topological defects. The focus of this high-precision Monte Carlo study is on the vortex network, which is…
We study phase transition in the ferromagnetic Potts model with invisible states that are added as redundant states by mean-field calculation and Monte Carlo simulation. Invisible states affect the entropy and the free energy, although they…
Finding suitable indicators for characterizing quantum phase transitions plays an important role in understanding different phases of matter. It is especially important for fracton phases where a combination of topology and…
In studies of the QCD deconfining phase transition or cross-over by means of heavy ion experiments, one ought to be concerned about non-equilibrium effects due to heating and cooling of the system. In this paper we extend our previous study…
The Potts model is a generalization of the Ising model with $Q>2$ components. In the fully connected ferromagnetic Potts model, a first-order phase transition is induced by varying thermal fluctuations. Therefore, the computational time…
We analyze the phase transitions that emerge from the recursive design of certain hyperbolic networks that includes, for instance, a discontinuous ("explosive") transition in ordinary percolation. To this end, we solve the $q$-state Potts…
We introduce a model for a population on a lattice with diffusion and birth/death according to 2A->3A and A->0 for a particle A. We find that the model displays a phase transition from an active to an absorbing state which is continuous in…