No Arabic abstract
In this work, we revisited the ZGB model in order to study the behavior of its phase diagram when two well-known random networks play the role of the catalytic surfaces: the Random Geometric Graph and the Erd{o}s-R{e}nyi network. The connectivity and, therefore, the average number of neighbors of the nodes of these networks can vary according to their control parameters, the neighborhood radius $alpha$ and the linking probability $p$, respectively. In addition, the catalytic reactions of the ZGB model are governed by the parameter $y$, the adsorption rate of carbon monoxide molecules on the catalytic surface. So, to study the phase diagrams of the model on both random networks, we carried out extensive steady-state Monte Carlo simulations in the space parameters ($y,alpha$) and ($y,p$) and showed that the continuous phase transition is greatly affected by the topological features of the networks while the discontinuous one remains present in the diagram throughout the interval of study.
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described by the topology of a network. We consider the q-state Potts model on an uncorrelated scale-free network for which the node-degree distribution manifests a power-law decay governed by the exponent lambda. We work within the mean-field approximation, since for systems on random uncorrelated scale-free networks this method is known to often give asymptotically exact results. Depending on particular values of q and lambda one observes either a first-order or a second-order phase transition or the system is ordered at any finite temperature. In a case study, we consider the limit q=1 (percolation) and find a correspondence between the magnetic exponents and those describing percolation on a scale-free network. Interestingly, logarithmic corrections to scaling appear at lambda=4 in this case.
The one-parametric Wang-Landau (WL) method is implemented together with an extrapolation scheme to yield approximations of the two-dimensional (exchange-energy, field-energy) density of states (DOS) of the 3D bimodal random-field Ising model (RFIM). The present approach generalizes our earlier WL implementations, by handling the final stage of the WL process as an entropic sampling scheme, appropriate for the recording of the required two-parametric histograms. We test the accuracy of the proposed extrapolation scheme and then apply it to study the size-shift behavior of the phase diagram of the 3D bimodal RFIM. We present a finite-size converging approach and a well-behaved sequence of estimates for the critical disorder strength. Their asymptotic shift-behavior yields the critical disorder strength and the associated correlation lengths exponent, in agreement with previous estimates from ground-state studies of the model.
We explore a class of random tensor network models with ``stabilizer local tensors which we name Random Stabilizer Tensor Networks (RSTNs). For RSTNs defined on a two-dimensional square lattice, we perform extensive numerical studies of entanglement phase transitions between volume-law and area-law entangled phases of the one-dimensional boundary states. These transitions occur when either (a) the bond dimension $D$ of the constituent tensors is varied, or (b) the tensor network is subject to random breaking of bulk bonds, implemented by forced measurements. In the absence of broken bonds, we find that the RSTN supports a volume-law entangled boundary state with bond dimension $Dgeq3$ where $D$ is a prime number, and an area-law entangled boundary state for $D=2$. Upon breaking bonds at random in the bulk with probability $p$, there exists a critical measurement rate $p_c$ for each $Dgeq 3$ above which the boundary state becomes area-law entangled. To explore the conformal invariance at these entanglement transitions for different prime $D$, we consider tensor networks on a finite rectangular geometry with a variety of boundary conditions, and extract universal operator scaling dimensions via extensive numerical calculations of the entanglement entropy, mutual information and mutual negativity at their respective critical points. Our results at large $D$ approach known universal data of percolation conformal field theory, while showing clear discrepancies at smaller $D$, suggesting a distinct entanglement transition universality class for each prime $D$. We further study universal entanglement properties in the volume-law phase and demonstrate quantitative agreement with the recently proposed description in terms of a directed polymer in a random environment.
We use a Monte Carlo bond-switching method to study systematically the thermodynamic properties of a continuous random network model, the canonical model for such amorphous systems as a-Si and a-SiO$_2$. Simulations show first-order melting into an amorphous state, and clear evidence for a glass transition in the supercooled liquid. The random-network model is also extended to study heterogeneous structures, such as the interface between amorphous and crystalline Si.
We study the effect of coadsorption of CO and O on a Ziff-Gulari-Barshad (ZGB) model with CO desorption (ZGB-d) for the reaction CO + O --> CO_2 on a catalytic surface. Coadsorption of CO on a surface site already occupied by an O is introduced by an Eley-Rideal-type mechanism that occurs with probability p, 0 <= p <= 1. We find that, besides the well known effect of eliminating the second-order phase transition between the reactive state and an O-poisoned state, the coadsorption step has a strong effect on the transition between the reactive state and the CO-poisoned state. The coexistence curve between these two states terminates at a critical value k_c of the desorption rate k which now depends on p. Our Monte Carlo simulations and finite-size scale analysis indicate that k_c decreases with increasing values of p. For p=1, there appears to be a sharp phase transition between the two states only for k at(or near) zero.