Related papers: Aperiodicity-Induced Second-Order Phase Transition…
We report on Monte Carlo simulations for the two-dimensional frustrated $J_1$-$J_2$ Ising model on the square lattice. Recent analysis has shown that for the phase transition from the paramagnetic state to the antiferromagnetic collinear…
We study dynamic behavior of Potts model with invisible states near the first-order phase transition temperature. We focus on melting process starting from the perfect ordered state. This model is regarded as a standard model to analyze…
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following two deterministic aperiodic sequences: Fibonacci or period-doubling ones. New algorithms of sequence generation were…
Critical behaviour of a system, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. Specifically, relaxational stochastic dynamics of a non-conserved multicomponent order…
We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts model. We find that the Li-Sokal bound ($\tau_{int,E} \geq const \times C_H$) is…
The q=10 and q=200 state Potts models coupled to 2d gravity are investigated numerically and shown to have continuous phase transitions, contrary to their behavior on a regular lattice. Critical exponents are extracted and possible critical…
The nonequilibrium dynamics of a cycling three-state Potts model is studied on a square lattice using Monte Carlo simulations and continuum theory. This model is relevant to chemical reactions on a catalytic surface and to molecular…
We use Monte Carlo simulations and finite-size scaling theory to investigate the phase transition and critical behavior of the $S$-state block voter model on square lattices. It is shown that the system exhibits an order-disorder phase…
This article studies the planar Potts model and its random-cluster representation. We show that the phase transition of the nearest-neighbor ferromagnetic $q$-state Potts model on $\mathbb Z^2$ is continuous for $q\in\{2,3,4\}$, in the…
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,…
We study the thermal phase transitions of the four-fold degenerate phases (the plaquette and single stripe states) in two-dimensional frustrated Ising model on the Shastry-Sutherland lattice using Monte Carlo simulations. The critical…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature/energy range around the critical point. By combining the replica-exchange algorithm with cluster updates…
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…
Using the Wang-Landau Monte Carlo method, we study the antiferromagnetic (AF) three-state Potts model with a staggered polarization field on the square lattice. We obtain two phase transitions; one belongs to the ferromagnetic three-state…
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…
We study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) $q$-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial…
We investigate the critical behaviour of the three-dimensional, three state Potts model in presence of a negative external field h, i.e. disfavouring one of the three states. A genuine phase transition is present for all values of |h|,…
We study the critical behavior of the random q-state Potts model in the large-q limit on the diamond hierarchical lattice with an effective dimensionality $d_{\rm eff} > 2$. By varying the temperature and the strength of the frustration the…
We present preliminary results of our numerical study of the critical dynamics of percolation observables for the two-dimensional Ising model. We consider the (Monte-Carlo) short-time evolution of the system obtained with a local heat-bath…
Understanding nonequilibrium systems and the consequences of irreversibility for the system's behavior as compared to the equilibrium case, is a fundamental question in statistical physics. Here, we investigate two types of nonequilbrium…