Excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit

We consider the random-bond Potts model in the large-$Q$ limit and calculate the excess entropy, $S_{\Gamma}$, of a contour, $\Gamma$, which is given by the mean number of Fortuin-Kasteleyn clusters which are crossed by $\Gamma$. In two dimensions $S_{\Gamma}$ is proportional to the length of $\Gamma$, to which - at the critical point - there are universal logarithmic corrections due to corners. These are calculated by applying techniques of conformal field theory and compared with the results of large scale numerical calculations. The central charge of the model is obtained from the corner contributions to the excess entropy and independently from the finite-size correction of the free-energy as: $\lim_{Q \to \infty}c(Q)/\ln Q =0.74(2)$, close to previous estimates calculated at finite values of $Q$.Comment: 6 pages, 7 figure

Finite size effects in ferromagnetic 3He nano-clusters

International audience3He adsorbed on Graphite enables to create model 2D ferromagnetic Heisenberg systems. The exchange énergies are of the order of 2mK, typical sizes on the order of a thousand spins. By adding 4He (which is non magnetic) to the system, one can tune the effective size of one ferromagnetic domain. Up to now, the theoretical tools available did not allow a quantitative understanding of themagnetism of these clusters. For the first time, "engineered" ferromagnetic nano-clusters are compared to accurate theoretical models in order to understand the finite size effects. The experimental magnetization of a cluster of about 16 spins is compared to exact diagonalization and Monte-Carlo simulations based on the Heisenberg Hamiltonian

Reentrant Random Quantum Ising Antiferromagnet

We consider the quantum Ising chain with uniformly distributed random antiferromagnetic couplings $(1 \le J_i \le 2)$ and uniformly distributed random transverse fields ($\Gamma_0 \le \Gamma_i \le 2\Gamma_0$) in the presence of a homogeneous longitudinal field, $h$. Using different numerical techniques (DMRG, combinatorial optimisation and strong disorder RG methods) we explore the phase diagram, which consists of an ordered and a disordered phase. At one end of the transition line ($h=0,\Gamma_0=1$) there is an infinite disorder quantum fixed point, while at the other end ($h=2,\Gamma_0=0$) there is a classical random first-order transition point. Close to this fixed point, for $h>2$ and $\Gamma_0>0$ there is a reentrant ordered phase, which is the result of quantum fluctuations by means of an order through disorder phenomenon.Comment: 10 pages, 7 figure

About the Yukawa model on a lattice in the quenched approximation

We study the Yukawa model on a 4-dimensional Euclidean lattice in the quenched approximation. A particular attention is given to the singularities of the Dirac operator in the phase diagram. A careful analysis of a particular limiting case shows that size effects can be huge, questioning the quenched approximation. This is confirmed by a Monte-Carlo simulation in this limit case and without the quenched approximation. We include also some results concerning the symmetries of this model.Comment: 7 figure

Statistics of percolating clusters in a model of photosynthetic bacteria

In photosynthetic organisms, the energy of light during illumination is absorbed by the antenna complexes, which is transmitted by excitons and is either absorbed by the reaction centers (RCs), which have been closed in this way, or emitted by fluorescence. The basic components of the dynamics of light absorption have been integrated into a simple model of exciton migration, which contains two parameters: the exciton hopping probability and the exciton lifetime. During continuous radiation with light the fraction of closed RCs, $x$, continuously increases and at a critical threshold, $x_c$, a percolation transition takes place. Performing extensive Monte Carlo simulations we study the properties of the transition in this correlated percolation model. We measure the spanning probability in the vicinity of $x_c$, as well as the fractal properties of the critical percolating cluster, both in the bulk and at the surface.Comment: 7 pages, 6 figure

Random-bond antiferromagnetic Ising model in a field

Using combinatorial optimisation techniques we study the critical properties of the two- and the three-dimensional Ising model with uniformly distributed random antiferromagnetic couplings $(1 \le J_i \le 2)$ in the presence of a homogeneous longitudinal field, $h$, at zero temperature. In finite systems of linear size, $L$, we measure the average correlation function, $C_L(\ell,h)$, when the sites are either on the same sub-lattice, or they belong to different sub-lattices. The phase transition, which is of first-order in the pure system, turns to mixed order in two dimensions with critical exponents $1/\nu \approx 0.5$ and $\eta \approx 0.7$. In three dimensions we obtain $1/\nu \approx 0.7$, which is compatible with the value of the random-field Ising model, but we cannot discriminate between second-order and mixed-order transitions.Comment: 6 pages, 5 figure

Phase transitions of the random-bond Potts chain with long-range interactions

International audienc

Scattering signatures of invasion percolation

International audienceMotivated by recent experiments, we investigate the scattering properties of percolation clustersgenerated by numerical simulations on a three dimensional cubic lattice. Individual clusters of given size are shown to present a fractal structure up to a scale of order their extent, even far away from the percolation threshold $p_c$. The influence of inter-cluster correlations on the structure factor of assemblies of clusters selected by an invasion phenomenon is studied in detail. For invasion from bulk germs, we show that the scattering properties are determined by three length scales, the correlation length $\xi$, the average distance between germs $d_g$, and the spatial scale probed by scattering, set by the inverse of the scattering wavevector $Q$. At small scales, we find that the fractal structure of individual clusters is retained, the structure factor decaying as $Q^{-d_f}$. At large scales, the structure factor tends to a limit, set by the smaller of $\xi$ and $d_g$, both below and above $p_c$. We propose approximate expressions reproducing the simulated structure factor for arbitrary $\xi$, $d_g$, and $Q$, and illustrate how they can be used to avoid to resort to costly numerical simulations. For invasion from surfaces, we find that, at $p_c$, the structure factor behaves as $Q^{-d_f}$ at all $Q$,\textit{ i.e.} the fractal structure is retained at arbitrarily large scales. Results away from $p_c$ are compared to the case of bulk germs. Our results can be applied to discuss light or neutrons scattering experiments on percolating systems. This is illustrated in the context of evaporation from porous materials

On Condensation and Evaporation Mechanisms in Disordered Porous Materials

International audienc