Related papers: Dynamical cluster size heterogeneity
A measure of cluster size heterogeneity ($H$), introduced by Lee et al [Phys. Rev. E {\bf 84}, 020101 (2011)] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising…
We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,...,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an…
Recently, a hybrid percolation transitions (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. In spite of considerable effort to develop the…
We study the geometric properties of a system initially in equilibrium at a critical point that is suddenly quenched to another critical point and subsequently evolves towards the new equilibrium state. We focus on the bidimensional Ising…
After a sudden quench from the disordered high-temperature $T_0\to\infty$ phase to a final temperature below the critical point $T_F \ll T_c$, the non-conserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a…
It is proposed that the $O(n)$ spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
We study nonequilibrium dynamical properties of inhomogeneous systems, in particular at a free surface or at a defect plane. Thereby we consider nonconserved (model-A) dynamics of a system which is prepared in the high-temperature phase and…
A hybrid percolation transition (HPT) exhibits both discontinuity of the order parameter and critical behavior at the transition point. Such dynamic transitions can occur in two ways: by cluster pruning with suppression of loop formation of…
We revisit here the problem of the collective non-equilibrium dynamics of a classical statistical system at a critical point and in the presence of surfaces. The effects of breaking separately space- and time-translational invariance are…
In supercooled liquids, mesoscale mobile and immobile domains are ubiquitously observed, a phenomenon known as dynamical heterogeneity. Extensive studies have established that the characteristic size of these domains grows upon cooling and…
We study dynamic heterogeneities in the out-of-equilibrium coarsening dynamics of the spherical ferromagnet after a quench from infinite temperature to its critical point. A standard way of probing such heterogeneities is by monitoring the…
We study the thermodynamics of the two-dimensional Hubbard model within the dynamical cluster approximation. We use continuous time quantum Monte Carlo as a cluster solver to avoid the systematic error which complicates the calculation of…
We present a systematic study of dynamical heterogeneity in a model for permanent gels, upon approaching the gelation threshold. We find that the fluctuations of the self intermediate scattering function are increasing functions of time,…
The dissipative nature of heat transfer relaxes thermal flows to an equilibrium state that is devoid of temperature gradients. The distance to reach an equilibrium temperature -- the thermal entrance length -- is a consequence of diffusion…
The non equilibrium relaxational dynamics of the solid on solid model on a disordered substrate and the Sine Gordon model with random phase shifts is studied numerically. Close to the super-roughening temperature $T_g$ our results for the…
We study the percolation properties of geometrical clusters defined in the overlap space of two statistically independent replicas of a square-lattice Ising model that are simulated at the same temperature. In particular, we consider two…
We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size which is typical of critical phenomena. Our approach is to introduce an external,…
Critical phenomena of a second-order percolation transition are known to be independent of cluster merging or pruning process. However, those of a hybrid percolation transition (HPT), mixed properties of both first-order and second-order…
Order parameter fluctuations (the largest cluster size distribution) are studied within a three-dimensional bond percolation model on small lattices. Cumulant ratios measuring the fluctuations exhibit distinct features near the percolation…