Related papers: Random trimer tilings
We present the results of an extension of our previous work on large-scale simulations of dynamically triangulated toroidal random surfaces embedded in $R^3$ with extrinsic curvature. We find that the extrinsic-curvature specific heat peak…
Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…
We develop Monte Carlo simulations for uniformly charged polymers and machine learning algorithm to interpret the intra-polymer structure factor of the charged polymer system, which can be obtained from small-angle scattering experiments.…
Relaxation rates in nearly integrable systems usually increase quadratically with the strength of the perturbation that breaks integrability. We show that the relaxation rates can be significantly smaller in systems that are integrable…
We consider local dynamics of the dimer model (perfect matchings) on hypercubic boxes $[n]^d$. These consist of successively switching the dimers along alternating cycles of prescribed (small) lengths. We study the connectivity properties…
The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a…
Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…
In this work, we investigate the classical loop models doped with monomers and dimers on a square lattice, whose partition function can be expressed as a tensor network (TN). In the thermodynamic limit, we use the boundary matrix product…
The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for non-concatenated unknotted rings, which are known to…
The wavelength of a periodic spatial structure of Turing type is an intrinsic property of the considered reaction-diffusion dynamics and we address the question of its control at the microscopic scale for given dynamical parameters. The…
We provide a proof that entanglement of any density matrix which block diagonal in subspaces which are disjoint in terms of the Hilbert space of one of the two potentially entangled subsystems can simply be calculated as the weighted…
Surfaces in i-Al68Pd23Mn9 as observed with STM and LEED experiments show atomic terraces in a Fibonacci spacing. We analyze them in a bulk tiling model due to Elser which incorporates many experimental data. The model has dodecahedral…
We explore the critical behaviour of two and three dimensional lattice models of polymers in dilute solution where the monomers carry a magnetic moment which interacts ferromagnetically with near-neighbour monomers. Specifically, the model…
We numerically study Turing patterns (TPs) on two-dimensional surfaces with a square boundary in ${\bf R}^3$ using a surface model for polymerized membranes. The variables used to describe the membranes correspond to two distinct degrees of…
The ground state entropy of the 2D Ising spin glass with +1 and -1 bonds is studied for $L \times M$ square lattices with $L \le M$ and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary…
We compute the bipartite entanglement properties of the spin-half square-lattice Heisenberg model by a variety of numerical techniques that include valence bond quantum Monte Carlo (QMC), stochastic series expansion QMC, high temperature…
We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases, goes through a minimum and…
The classical monomer-dimer model in two-dimensional lattices has been shown to belong to the \emph{``#P-complete''} class, which indicates the problem is computationally ``intractable''. We use exact computational method to investigate the…
We propose a lattice model for Dirac fermions which allows us to break the degeneracy of the node structure. In the presence of a random gap we analyze the scaling behavior of the localization length as a function of the system width within…
The process of adsorption on a planar repulsive, "marginal" and attractive wall of long-flexible polymer chains with excluded volume interactions is investigated. The performed scaling analysis is based on formal analogy between the polymer…