Based on the difference between a spanning cluster and a wrapping cluster, an alternative criterion for testing wrapping percolation is provided for two-dimensional lattices. By following the Newman-Ziff method, the finite size scalings of estimates for percolation thresholds are given. The results are consistent with those from Machta's method.
Recent experiments on quantum walks (QWs) of a single and two particles demonstrated subtle quantum statistics-dependent walks in one-dimensional (1D) lattices. However the roles of interaction and quantum statistics in such a kind of walks are little known at a many-body level. In this letter, using time-evolving block decimation algorithm and many-body perturbation theory we rigorously study QWs, Bloch oscillations and quantum Fisher informations (FIs) for three indistinguishable bosons and fermions in 1D lattices. We show that such strongly correlated many-body QWs not only give rise to statistics-and-interaction-dependent ballistic transports of scattering states, two-and three-body bound states, but also present a quantum enhanced precision measurement of the gravitational force. It turns out that in contrast to the walks of the fermions, the QWs of three bosons exhibit richer dynamics of co-walkings and competitive Bloch oscillations, which remarkably present a surprising time scaling t 3 of FI below a characteristic time t0 and saturate to the fundamental limit of t 2 for t > t0.
Percolation, characterizing the emergence of large-scale connectivity from a great number of isolated nodes, can generate continuous, multiple discontinuous and discontinuous phase transitions, which correspond to different physical processes, respectively. In this paper, we found a percolation model which unifies all the three types of phase transitions with a continuously tunable parameter α. When decreasing α from 1 to 0, the type of phase transition transfers from continuous to multiple discontinuous, and finally the percolation process exhibits a single discontinuity lacking a supercritical region. By carefully examining the evolving characteristic of the clusters, it is verified that the transition value of α is between 0.75 and 0.7 for the phase transition from continuous to multiple discontinuous, and the distinctly different behaviors of the relative variance of the order parameter at and confirm the result. On the other hand, the transition value of α is 0.5 at which the type of phase transition changes from multiple discontinuous to discontinuous. These results may be helpful in understanding the physical mechanisms behind various percolation transition processes.
Treating the bilocal quark-quark interaction kernel as an input parameter, the self-energy functions can be determined from the "rainbow" Dyson-Schwinger equation, which is obtained in the global color symmetry model. The tensor susceptibility of QCD vacuum can be calculated directly from these self-energy functions. The values we obtained are much smaller than the estimations from QCD sum rules and from chiral constituent quark model.
We propose two schemes to achieve fast realizations of spatially correlated percolation models. The schemes are shown to be efficient in complementary regimes of correlation phase space. They are combined with a generalized Newman-Ziff algorithm to numerically determine the percolation thresholds of two-dimensional lattices in the presence of correlations. It is found that the spatial correlations affect only a relatively small part of phase space.
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