Related papers: Results and conjectures on a toy model of depinnin…
We introduce a toy model, which represents a simplified version of the problem of the depinning transition in the limit of strong disorder. This toy model can be formulated as a simple renormalization transformation for the probability…
We investigate the recently proposed dimensional reduction conjecture in driven disordered systems using a machine learning technique. The conjecture states that a static snapshot of a disordered system driven at a constant velocity is…
The Derrida--Retaux recursive system was investigated by Derrida and Retaux (2014) as a hierarchical renormalization model in statistical physics. A prediction of Derrida and Retaux (2014) on the free energy has recently been rigorously…
We perform Monte Carlo simulations to study the two dimensional random-bond XY model on a square lattice. Two kinds of bond randomness with the coupling coefficient obeying the Gaussian or uniform distribution are discussed. It is shown…
We consider a renewal process \tau={\tau_0,\tau_1,...} on the integers, where the law of \tau_i-\tau_{i-1} has a power-like tail P(\tau_i-\tau_{i-1}=n)=n^{-(\alpha+1)}L(n) with \alpha\ge0 and L(.) slowly varying. We then assign a random,…
We study the phase transition between conducting and insulating states taking place in disordered multi-channel Luttinger liquids with inter-channel interactions. We derive renormalisation group equations which are perturbative in disorder…
Interfaces advancing through random media represent a number of different problems in physics, biology and other disciplines. Here, we study the pinning/depinning transition of the prototypical non-equilibrium interfacial model, i.e. the…
With the recent developments in machine learning, Carrasquilla and Melko have proposed a paradigm that is complementary to the conventional approach for the study of spin models. As an alternative to investigating the thermal average of…
We consider a 2D XY model subjected to time-correlated noise, a model of direct relevance to active crystals, which were shown recently to be able to support very large deformations without melting in the presence of persistent…
The possibi;lity of a probabilistic interpretation is studied for the Regge-Gribov model in zero dimensional transverse world ("Toy") with interacting pomerons and odderons. It is found that the previously proposed recipe to introduce such…
We give an overview of the state of the art of the analysis of disordered models of pinning on a defect line. This class of models includes a number of well known and much studied systems (like polymer pinning on a defect line, wetting of…
We study the triangular lattice Ising model with a finite number of vertically stacked layers and demonstrate a low temperature reentrance of two Berezinskii-Kosterlitz-Thouless transitions, which results in an extended disordered regime…
In statistical physics, the XY model in two dimensions provides the paradigmatic example of phase transitions mediated by topological defects (vortices). Over the years, a variety of analytical and numerical methods have been deployed in an…
We study the depinning transition of a driven chain-like system in the presence of frustration and quenched disorder. The analysis is motivated by recent transport experiments on artificial vortex-flow channels in superconducting thin…
To study the depinning transition in the limit of strong disorder, Derrida and Retaux (2014) introduced a discrete-time max-type recursive model. It is believed that for a large class of recursive models, including Derrida and Retaux'…
When a disordered solid is sheared, yielding is followed by the onset of intermittent response that is characterized by slip in local regions usually labeled shear-transformation zones (STZ). Such intermittent response resembles the…
Periodic boundary conditions are not always used in the study of disordered systems, but it can be advantageous to apply them to mimick thermodynamically large systems. In this case, polarization and its cumulants can not be obtained…
The nature of the interplay between fluctuations and quenched random disorder is a long-standing open problem, particularly in systems with a continuous order parameter. This lack of a full theoretical treatment has been underscored by…
The Berezinski-Kosterlitz-Thouless transition is a unique two dimensional phase transition, separating two phases with exponentially and power-law decaying correlations, respectively. In disordered systems, these correlations propagate…
We show, that the 2D XY-model with random phase shifts exhibits for low temperature and small disorder a phase with quasi-long-range order, and that the transition to the disordered phase is {\it not} reentrant. These results are obtained…