Jamming probabilities for a vacancy in the dimer model

Moving Vortex Phases, Dynamical Symmetry Breaking, and Jamming for Vortices in Honeycomb Pinning Arrays

We show using numerical simulations that vortices in honeycomb pinning arrays can exhibit a remarkable variety of dynamical phases that are distinct from those found for triangular and square pinning arrays. In the honeycomb arrays, it is possible for the interstitial vortices to form dimer or higher n-mer states which have an additional orientational degree of freedom that can lead to the formation of vortex molecular crystals. For filling fractions where dimer states appear, a novel dynamical symmetry breaking can occur when the dimers flow in one of two possible alignment directions. This l…

Vacancy localization in the square dimer model

We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this formalism, we can address the question of the possible motion of the vacancy induced by dimer slidings. We find a probability 57/4-10Sqrt[2] for the vacancy to be strictly jammed in an infinite system. More generally, the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9/8. On a finite system, the prob…

Dimer Statistics on a Bethe Lattice

We discuss the exact solutions of various models of the statistics of dimer coverings of a Bethe lattice. We reproduce the well-known exact results for noninteracting hard-core dimers by both a very simple geometrical argument and a general algebraic formulation for lattice statistical problems. For the Bethe lattice we also obtain the exact solution when either a) the dimers interact via a short-range interaction or b) the underlying lattice is anisotropic. We also give solutions for special cases of random lattices and for the jamming limit of one dimensional deposition of dimers.

On the fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media

The fluctuations of the jamming coverage upon Random Sequential Adsorption (RSA) are studied using both analytical and numerical techniques. Our main result shows that these fluctuations (characterized by $σ_{θ_J}$) decay with the lattice size according to the power-law $σ_{θ_J} \propto L^{-1/ ν}$. The exponent $ν$ depends on the dimensionality $D$ of the substrate and the fractal dimension of the set where the RSA process actually takes place ($d_f$) according to $ν= 2 / (2D - d_f)$.This theoretical result is confirmed by means of extensive numerical simulations applied to the RSA of dimers o…

Percolation of the aligned dimers on a square lattice

Percolation and jamming phenomena are investigated for anisotropic sequential deposition of dimers (particles occupying two adjacent adsorption sites) on a square lattice. The influence of dimer alignment on the electrical conductivity was examined. The percolation threshold for deposition of dimers was lower than for deposition of monomers. Nevertheless, the problem belongs to the universality class of random percolation. The lowest percolation threshold (pc = 0.562) was observed for isotropic orientation of dimers. It was higher (pc = 0.586) in the case of dimers aligned strictly along one d…

Random sequential adsorption and diffusion of dimers and k-mers on a square lattice

We have performed extensive simulations of random sequential adsorption and diffusion of $k$-mers, up to $k=5$ in two dimensions with particular attention to the case $k=2$. We focus on the behavior of the coverage and of vacancy dynamics as a function of time. We observe that for $k=2,3$ a complete coverage of the lattice is never reached, because of the existence of frozen configurations that prevent isolated vacancies in the lattice to join. From this result we argue that complete coverage is never attained for any value of $k$. The long time behavior of the coverage is not mean field and n…

Breaking universality in random sequential adsorption on a square lattice with long-range correlated defects

Jamming and percolation transitions in the standard random sequential adsorption of particles on regular lattices are characterized by a universal set of critical exponents. The universality class is preserved even in the presence of randomly distributed defective sites that are forbidden for particle deposition. However, using large-scale Monte Carlo simulations by depositing dimers on the square lattice and employing finite-size scaling, we provide evidence that the system does not exhibit such well-known universal features when the defects have spatial long-range (power-law) correlations. T…

在 $(2p + 1) \times (2q + 1)$ 格点上堆积二聚体

Packing dimers on $(2p + 1) \times (2q + 1) $ lattices

本研究通过计算方法探讨奇数乘奇数格点上的二聚体堆积，发现其构型数具有数论性质，并证明自由能修正中存在对数项，揭示了统计物理与数论的新联系，暗示单体-二聚体问题可能可解。

Random sequential adsorption of straight rigid rods on a simple cubic lattice

Random sequential adsorption of straight rigid rods of length $k$ ($k$-mers) on a simple cubic lattice has been studied by numerical simulations and finite-size scaling analysis. The calculations were performed by using a new theoretical scheme, whose accuracy was verified by comparison with rigorous analytical data. The results, obtained for \textit{k} ranging from 2 to 64, revealed that (i) in the case of dimers ($k=2$), the jamming coverage is $θ_j=0.918388(16)$. Our estimate of $θ_j$ differs significantly from the previously reported value of $θ_j=0.799(2)$ [Y. Y. Tarasevich and V. A. Cher…

带隙短程共振价键自旋液体中非磁性杂质的磁效应

Magnetic effects of non-magnetic impurities in gapped short-range resonating valence bond spin liquids

本研究探讨了非磁性杂质对带隙短程RVB自旋液体和VBS态的磁效应，发现kagome晶格上的RVB液体在小杂质密度下稳定，而其他晶格的RVB态及VBS态均不稳定，该结论得到计算结果支持。