Related papers: 2D additive small-world network with distance-depe…
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor…
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
This work considers an Ising model on the Apollonian network, where the exchange constant $J_{i,j}\sim1/(k_ik_j)^\mu$ between two neighboring spins $(i,j)$ is a function of the degree $k$ of both spins. Using the exact geometrical…
We study the effect of long-range connections on the infinite-randomness fixed point associated with the quantum phase transitions in a transverse Ising model (TIM). The TIM resides on a long-range connected lattice where any two sites at a…
We present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an absorbing-state phase transition at a finite critical value of the control parameter,…
We explore the coupled dynamics of the internal states of a set of interacting elements and the network of interactions among them. Interactions are modeled by a spatial game and the network of interaction links evolves adapting to the…
Accurate numerical results are presented for the three-dimensional equivalent-neighbor model on a cubic lattice, for twelve different interaction ranges (coordination number between 18 and 250). These results allow the determination of the…
The Ising model in a random field and with power-law decaying ferromagnetic bonds is studied at zero temperature. Comparing the scaling of the energy contributions of the ferromagnetic domain wall flip and of the random field a la Imry-Ma…
In this thesis, we present results on phase transition for two models: the semi-infinite Ising model with a decaying field, and the long-range Ising model with a random field. We study the semi-infinite Ising model with an external field…
We studied the critical behavior of the $J_{1}-J_{2}$ spin-{1/2} Ising model in the square lattice by considering $J_{1}$ fixed and $J_{2}$ as random interactions following discrete and continuous probability distribution functions. The…
Two new classes of networks are introduced that resemble small-world properties. These networks are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical…
The Ising model on a $restricted$ scale-free network (SFN) has been studied employing Monte Carlo simulations. This network is described by a power-law degree distribution in the form $P(k)~k^{-\alpha}$, and is called restricted, because…
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…
Like other social animals and biological systems, human groups constantly exchange information. Network models provide a way of quantifying this process by representing the pathways of information propagation between individuals. Existing…
We study damage-spreading in the ferromagnetic Ising model on small world networks using Monte Carlo simulation with Glauber dynamics. The damage spreading temperature $T_d$ is determined as a function of rewiring probability $p$ for small…
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the…
We investigate three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling. These models are the spin-1/2 Ising model with nearest-neighbor interactions, a spin-1/2 model with nearest-neighbor and…
We study the dynamics of a spin facilitated Ising model with long range kinetic constraints. To formulate those restrictions within an analytical approach we introduce the size of a kinetic active environment of a given spin. Based on a…
We present the results of extensive Monte Carlo simulations of Ising models with algebraically decaying ferromagnetic interactions in the regime where classical critical behavior is expected for these systems. We corroborate the values for…
We analyze a generalization of the hard sphere dipole system in two dimensions in which the interaction range of the interaction can be varied. We focus on the system in the limit the interaction becomes increasingly short-ranged, while the…