Related papers: Ising and Potts Models on Quenched Random Gravity …
We introduce an exact replica method for the study of critical systems with quenched bond randomness in two dimensions. For the $q$-state Potts model we show that a line of renormalization group fixed points interpolates from weak to strong…
We consider the fractal dimensions of critical clusters occurring in configurations of a q-state Potts model coupled to the planar random graphs of the dynamical triangulations formulation of Euclidean quantum gravity in two dimensions. For…
Machine-learning (ML) models trained on Ising spin configurations have demonstrated surprising effectiveness in classifying phases of Potts models, even when processing severely reduced representations that retain only two spin states. To…
Generalizing the mapping between the Potts model with nearest neighbor interaction and six vertex model, we build a family of "fused Potts models" related to the spin $k/2$ ${\rm U}_{q}{\rm su}(2)$ invariant vertex model and quantum spin…
Using a Wang-Landau entropic sampling scheme, we investigate the effects of quenched bond randomness on a particular case of a triangular Ising model with nearest- ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$) antiferromagnetic…
We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit…
We consider the Ising model for two interacting groups of spins embedded in an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the…
The main goal of the paper is to prove central limit theorems for the magnetization rescaled by $\sqrt{N}$ for the Ising model on random graphs with $N$ vertices. Both random quenched and averaged quenched measures are considered. We work…
We consider the Ising, and more generally, $q$-state Potts Glauber dynamics on random $d$-regular graphs on $n$ vertices at low temperatures $\beta \gtrsim \frac{\log d}{d}$. The mixing time is exponential in $n$ due to a bottleneck between…
We study the nonequilibrium dynamics of the $q$-state Potts model following a quench from the high temperature disordered phase to zero temperature. The time dependent two-point correlation functions of the order parameter field satisfy…
Changes in magnetic critical behaviour of quenched structurally-disordered magnets are usually exemplified in experiments and in MC simulations by diluted systems consisting of magnetic and non-magnetic components. By our study we aim to…
We investigate the effects of quenched bond randomness on the critical properties of the two-dimensional ferromagnetic Ising model embedded in a triangular lattice. The system is studied in both the pure and disordered versions by the same…
We investigate the dynamical critical behavior of the two-dimensional three-state Potts model with single spin-flip dynamics in equilibrium. We focus on the mean-squared deviation of the magnetization $M$ (MSD$_{M}$) as a function of time,…
The two-dimensional random-bond Q-state Potts model is studied for Q near 2 via the perturbative renormalisation group to one loop. It is shown that weak disorder induces cross-correlations between the quenched-averages of moments of the…
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…
Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing…
Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between…
We investigate the effect of quenched bond disorder on the two-dimensional three-color Ashkin-Teller model, which undergoes a first-order phase transition in the absence of impurities. This is one of the simplest and striking models in…
We present an extensive study of the effects of quenched disorder on the dynamic phase transitions of kinetic spin models in two dimensions. We undertake a numerical experiment performing Monte Carlo simulations of the square-lattice…
The critical properties of the 2D Ising and 3-state Potts models are investigated using Monte Carlo simulations. Special interest is given to measurement of 3-point correlation functions and associated universal objects, i.e. structure…