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Purely entropic systems such as suspensions of hard rods, platelets and spheres show rich phase behavior. Rods and platelets have successfully been used as models to predict the equilibrium properties of liquid crystals for several decades.…
The competition between local Brownian roughness and global parabolic curvature experienced in many random interface models reflects an important aspect of the KPZ universality class. It may be summarised by an exponent triple…
In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square,…
We study with lattice Monte Carlo simulations the relation of global O(2) symmetry breaking in three dimensions to the properties of a geometrically defined vortex loop network. We find that different definitions of constructing a network…
Numerical simulations and finite-size scaling analysis have been carried out to study the percolation behavior of straight rigid rods of length $k$ ($k$-mers) on two-dimensional square lattices. The $k$-mers, containing $k$ identical units…
We comment on the nature of the ordering transition of a model of equilibrium polydisperse rigid rods, on the square lattice, which is reported by Lopez et al. to exhibit random percolation criticality in the canonical ensemble, in sharp…
We study percolation as a critical phenomenon on a multifractal support. The scaling exponents of the the infinite cluster size ($\beta$ exponent) and the fractal dimension of the percolation cluster ($d_f$) are quantities that seem do not…
We investigate the percolation transition of aligned, overlapping, anisotropic shapes on lattices. Using the recently proposed lattice version of excluded volume theory, we show that shape-anisotropy leads to some intriguing consequences…
We present a general scaling theory for the surface critical behavior of non-equilibrium systems with phase transitions into absorbing states. The theory allows for two independent surface exponents which satisfy generalized hyperscaling…
We introduce and solve a model of hardcore particles on a one dimensional periodic lattice which undergoes an active-absorbing state phase transition at finite density. In this model an occupied site is defined to be active if its left…
We study the full class of kinetically constrained models in arbitrary dimension and out of equilibrium, in the regime where the density $q$ of facilitating sites in the equilibrium measure (but not necessarily in the initial measure) is…
We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modellized by hard-core spherical particles surrounded by penetrable…
By means of numerical simulations we investigate the geometric properties of loops on hypercubic lattice graphs in dimensions d=2 through 7, where edge weights are drawn from a distribution that allows for positive and negative weights. We…
We study a dependent site percolation model on the $n$-dimensional Euclidean lattice where, instead of single sites, entire hyperplanes are removed independently at random. We extend the results about Bernoulli line percolation showing that…
Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model…
We consider a directed variant of the negative-weight percolation model in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values.…
We (1) construct a one-parameter family of lattice models of interacting spins; (2) obtain their exact ground states; (3) derive a statistical-mechanical analogy which relates their ground states to O(n) loop gases; (4) show that the models…
Phase transitions to absorbing states are among the simplest examples of critical phenomena out of equilibrium. The characteristic feature of these models is the presence of a fluctuationless configuration which the dynamics cannot leave,…
Numerical investigation of critical exponents on a hypercubic with L^d random sites with L up to $33 and d up to 7 show that above the critical dimension the phase transitions in Ising model and percolation are not alike.
The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation…