Related papers: Invaded cluster algorithm for equilibrium critical…

We consider the integrable family of symmetric boundary-driven interacting particle systems that arise from the non-compact XXX Heisenberg model in one dimension with open boundaries. In contrast to the well-known symmetric exclusion…

The critical behaviour of several spin models can be simply described as percolation of some suitably defined clusters, or droplets: the onset of the geometrical transition coincides with the critical point and the percolation exponents are…

For a second-order phase transition the critical energy range of interest is larger than the energy range covered by a canonical Monte Carlo simulation at the critical temperature. Such an extended energy range can be covered by performing…

We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like anti-ferromagnetic interaction. We compute free energy, spin correlation functions and entanglement both in the ground and in…

We study a class of 2D non-equilibrium Ising models based on competing dynamics induced by contact with heat-baths at two different temperatures. We make a comparative study of the non-equilibrium versions of Metropolis, heat bath/Glauber…

A new kind of invasion percolation is introduced in order to take into account the inertia of the invader fluid. The inertia strength is controlled by the number N of pores (or steps) invaded after the perimeter rupture. The new model…

We study two-dimensional Ising spins, evolving through reinforcement learning using their state, action, and reward. The state of a spin is defined as whether it is in the majority or minority with its nearest neighbours. The spin updates…

We use a non-equilibrium simulation method to study the spin glass transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo…

It was recently shown that entanglement in quantum systems being in a non-equilibrium state can appear at much higher temperatures than in an equilibrium state. However, any system is subject to the natural relaxation process establishing…

We study invasion percolation in two dimensions, focusing on properties of the outlets of the invasion and their relation to critical percolation and to incipient infinite clusters (IIC's). First we compute the exact decay rate of the…

We present a new, simple, fast algorithm to numerically evolve disks of inelastically colliding particles surrounding a central star. Our algorithm adds negligible computational cost to the fastest existing collisionless N-body codes, and…

We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…

In random percolation one finds that the mean field regime above the upper critical dimension can simply be explained through the coexistence of infinite percolating clusters at the critical point. Because of the mapping between percolation…

Quantum spin systems with strong geometric restrictions give rise to rich quantum phases such as valence bond solids and spin liquid states. However, the geometric restrictions often hamper the application of sophisticated numerical…

We study the boundary effects in invasion percolation with and without trapping. We find that the presence of boundaries introduces a new set of surface critical exponents, as in the case of standard percolation. Numerical simulations show…

Clusters and droplets of positive spins in the two-dimensional Ising model percolate at the Curie temperature in absence of external field. The percolative exponents coincide with the magnetic ones for droplets but not for clusters. We use…

We analyze the recently developed folding algorithm [Phys. Rev. Lett. 102, 240603 (2009)] to simulate the dynamics of infinite quantum spin chains, and relate its performance to the kind of entanglement produced under the evolution of…

The generalization of Kasteleyn and Fortuin clusters formalism is introduced in XY (or more generally O(n)) models. Clusters geometrical structure may be linked to spin physical properties as correlation functions. To investigate…

We discuss a new Monte Carlo algorithm for the simulation of complex fluids. This algorithm employs geometric operations to identify clusters of particles that can be moved in a rejection-free way. It is demonstrated that this geometric…

In this thesis, we propose several modelling strategies to tackle evolving data in different contexts. In the framework of static clustering, we start by introducing a soft kernel spectral clustering (SKSC) algorithm, which can better deal…