Ising model on the Apollonian network with node dependent interactions

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 construction rule for the network, the thermodynamical and magnetic properties are evaluated by iterating a system of discrete maps that allows for very precise results in the thermodynamic limit. The results can be compared to the predictions of a general framework for spins models on scale-free networks, where the node distribution $P(k)\sim k^{-\gamma}$, with node dependent interacting constants. We observe that, by increasing $\mu$, the critical behavior of the model changes, from a phase transition at $T=\infty$ for a uniform system $(\mu=0)$, to a T=0 phase transition when $\mu=1$: in the thermodynamic limit, the system shows no exactly critical behavior at a finite temperature. The magnetization and magnetic susceptibility are found to present non-critical scaling properties.Comment: 6 figures, 12 figure file

Cuscuton kinks and branes

In this paper, we study a peculiar model for the scalar field. We add the cuscuton term in a standard model and investigate how this inclusion modifies the usual behavior of kinks. We find the first order equations and calculate the energy density and the total energy of the system. Also, we investigate the linear stability of the model, which is governed by a Sturm-Liouville eigenvalue equation that can be transformed in an equation of the Shcr\"odinger type. The model is also investigated in the braneworld scenario, where a first order formalism is also obtained and the linear stability is investigated.Comment: 21 pages, 9 figures; content added; to appear in NP

On the necessity to include event-by-event fluctuations in experimental evaluation of elliptical flow

Elliptic flow at RHIC is computed event-by-event with NeXSPheRIO. We show that when symmetry of the particle distribution in relation to the reaction plane is assumed, as usually done in the experimental extraction of elliptic flow, there is a disagreement between the true and reconstructed elliptic flows (15-30% for $\eta$=0, 30% for $p_\perp$=0.5 GeV). We suggest a possible way to take into account the asymmetry and get good agreement between these elliptic flows

Einstein-Maxwell Dirichlet walls, negative kinetic energies, and the adiabatic approximation for extreme black holes

The gravitational Dirichlet problem -- in which the induced metric is fixed on boundaries at finite distance from the bulk -- is related to simple notions of UV cutoffs in gauge/gravity duality and appears in discussions relating the low-energy behavior of gravity to fluid dynamics. We study the Einstein-Maxwell version of this problem, in which the induced Maxwell potential on the wall is also fixed. For flat walls in otherwise-asymptotically-flat spacetimes, we identify a moduli space of Majumdar-Papapetrou-like static solutions parametrized by the location of an extreme black hole relative to the wall. Such solutions may be described as balancing gravitational repulsion from a negative-mass image-source against electrostatic attraction to an oppositely-signed image charge. Standard techniques for handling divergences yield a moduli space metric with an eigenvalue that becomes negative near the wall, indicating a region of negative kinetic energy and suggesting that the Hamiltonian may be unbounded below. One may also surround the black hole with an additional (roughly spherical) Dirichlet wall to impose a regulator whose physics is more clear. Negative kinetic energies remain, though new terms do appear in the moduli-space metric. The regulator-dependence indicates that the adiabatic approximation may be ill-defined for classical extreme black holes with Dirichlet walls.Comment: 29 pages, 3 figures. v3: made minor corrections to agree with published version, v2: added a brief discussion of the Landau-Lifshtiz technique on page 1

Analytical approach to directed sandpile models on the Apollonian network

We investigate a set of directed sandpile models on the Apollonian network, which are inspired on the work by Dhar and Ramaswamy (PRL \textbf{63}, 1659 (1989)) for Euclidian lattices. They are characterized by a single parameter $q$, that restricts the number of neighbors receiving grains from a toppling node. Due to the geometry of the network, two and three point correlation functions are amenable to exact treatment, leading to analytical results for the avalanche distributions in the limit of an infinite system, for $q=1,2$. The exact recurrence expressions for the correlation functions are numerically iterated to obtain results for finite size systems, when larger values of $q$ are considered. Finally, a detailed description of the local flux properties is provided by a multifractal scaling analysis.Comment: 7 pages in two-column format, 10 illustrations, 5 figure

Critical exponents for the long-range Ising chain using a transfer matrix approach

The critical behavior of the Ising chain with long-range ferromagnetic interactions decaying with distance $r^\alpha$, $1<\alpha<2$, is investigated using a numerically efficient transfer matrix (TM) method. Finite size approximations to the infinite chain are considered, in which both the number of spins and the number of interaction constants can be independently increased. Systems with interactions between spins up to 18 sites apart and up to 2500 spins in the chain are considered. We obtain data for the critical exponents $\nu$ associated with the correlation length based on the Finite Range Scaling (FRS) hypothesis. FRS expressions require the evaluation of derivatives of the thermodynamical properties, which are obtained with the help of analytical recurrence expressions obtained within the TM framework. The Van den Broeck extrapolation procedure is applied in order to estimate the convergence of the exponents. The TM procedure reduces the dimension of the matrices and circumvents several numerical matrix operations.Comment: 10 pages, 2 figures, Conference NEXT Sigma Ph

Eccentricity fluctuations in an integrated hybrid approach: Influence on elliptic flow

The effects of initial state fluctuations on elliptic flow are investigated within a (3+1)d Boltzmann + hydrodynamics transport approach. The spatial eccentricity ($\epsilon_{\rm RP}$ and $\epsilon_{\rm part}$) is calculated for initial conditions generated by a hadronic transport approach (UrQMD). Elliptic flow results as a function of impact parameter, beam energy and transverse momentum for two different equations of state and for averaged initial conditions or a full event-by-event setup are presented. These investigations allow the conclusion that in mid-central ($b=5-9$ fm) heavy ion collisions the final elliptic flow is independent of the initial state fluctuations and the equation of state. Furthermore, it is demonstrated that most of the $v_2$ is build up during the hydrodynamic stage of the evolution. Therefore, the use of averaged initial profiles does not contribute to the uncertainties of the extraction of transport properties of hot and dense QCD matter based on viscous hydrodynamic calculations.Comment: 7 pages, 7 figures, minor revision of figures and conclusion, as published in PR