ترغب بنشر مسار تعليمي؟ اضغط هنا

Percolation phase transition by removal of $k^{2}$-mers from fully occupied lattices

68   0   0.0 ( 0 )
 نشر من قبل Luc\\'ia Ramirez
 تاريخ النشر 2019
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse site percolation by the removal of $k times k$ square tiles ($k^{2}$-mers) from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by occupied sites. Then, the system is diluted by removing $k^{2}$-mers of occupied sites from the lattice following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be removed due to the absence of occupied sites clusters of appropriate size and shape. The central idea of this paper is based on finding the maximum concentration of occupied sites, $p_{c,k}$, for which the connectivity disappears. This particular value of the concentration is called textit{inverse percolation threshold}, and determines a well-defined geometrical phase transition in the system. The results obtained for $p_{c,k}$ show that the inverse percolation threshold is a decreasing function of $k$ in the range $1 leq k leq 4$. For $k geq 5$, all jammed configurations are percolating states, and consequently, there is no non-percolating phase. In other words, the lattice remains connected even when the highest allowed concentration of removed sites is reached. The jamming exponent $ u_j$ was measured, being $ u_j = 1$ regardless of the size $k$ considered. In addition, the accurate determination of the critical exponents $ u$, $beta$ and $gamma$ reveals that the percolation phase transition involved in the system, which occurs for $k$ varying between 1 and 4, has the same universality class as the standard percolation problem.



قيم البحث

اقرأ أيضاً

168 - Bijoy Daga , P. K. Mohanty 2014
We introduce a driven diffusive model involving poly-dispersed hard k-mers on a one dimensional periodic ring and investigate the possibility of phase separation transition in such systems. The dynamics consists of a size dependent directional drive and reconstitution of k-mers. The reconstitution dynamics constrained to occur among consecutive immobile k-mers allows them to change their size while keeping the total number of k-mers and the volume occupied by them conserved. We show by mapping the model to a two species misanthrope process that its steady state has a factorized form. Along with a fluid phase, the interplay of drift and reconstitution can generate a macroscopic k-mer, or a slow moving k-mer with a macroscopic void in front of it, or both. We demonstrate this phenomenon for some specific choice of drift and reconstitution rates and provide exact phase boundaries which separate the four phases.
68 - Loic Turban 2019
We study the random sequential adsorption of $k$-mers on the fully-connected lattice with $N=kn$ sites. The probability distribution $T_n(s,t)$ of the time $t$ needed to cover the lattice with $s$ $k$-mers is obtained using a generating function appr oach. In the low coverage scaling limit where $s,n,ttoinfty$ with $y=s/n^{1/2}={mathrm O}(1)$ the random variable $t-s$ follows a Poisson distribution with mean $ky^2/2$. In the intermediate coverage scaling limit, when both $s$ and $n-s$ are ${mathrm O}(n)$, the mean value and the variance of the covering time are growing as $n$ and the fluctuations are Gaussian. When full coverage is approached the scaling functions diverge, which is the signal of a new scaling behaviour. Indeed, when $u=n-s={mathrm O}(1)$, the mean value of the covering time grows as $n^k$ and the variance as $n^{2k}$, thus $t$ is strongly fluctuating and no longer self-averaging. In this scaling regime the fluctuations are governed, for each value of $k$, by a different extreme value distribution, indexed by $u$. Explicit results are obtained for monomers (generalized Gumbel distribution) and dimers.
142 - Urna Basu , P. K. Mohanty 2009
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 neighbour is o ccupied and the right neighbour is vacant. Particles from such active sites hop stochastically to their right. We show that, both the density of active sites and the survival probability vanish as the particle density is decreased below half. The critical exponents and spatial correlations of the model are calculated exactly using the matrix product ansatz. Exact analytical study of several variations of the model reveals that these non-equilibrium phase transitions belong to a new universality class different from the generic active-absorbing-state phase transition, namely directed percolation.
176 - Sang-Woo Kim , Jae Dong Noh 2008
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network undergoes a pe rcolation transition. The percolation transition is characterized by a weak singular behavior of the mean cluster size and power-law scalings of the percolation order parameter and the cluster size distribution in the entire non-percolating phase. These results suggest that the assortative degree-degree correlation generates a global structural correlation which is relevant to the percolation critical phenomena of complex networks.
The mixed spin-(1/2, 1) Ising model on two fully frustrated triangles-in-triangles lattices is exactly solved with the help of the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the equivalent spin- 1/2 Ising model on a triangular lattice. It is shown that the mutual interplay between the spin frustration and single-ion anisotropy gives rise to various spontaneously ordered and disordered ground states, which differ mainly in an occurrence probability of the non-magnetic spin state of the integer-valued decorating spins. We have convincingly evidenced a possible coexistence of the spontaneous long-range order with a partial disorder within the striking ordered-disordered ground state, which manifest itself through a non-trivial criticality at finite temperatures as well. A rather rich critical behaviour including the order-from-disorder effect and reentrant phase transitions with either two or three successive critical points is also found.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا