Contact process on a Voronoi triangulation

Percolation thresholds on 2D Voronoi networks and Delaunay triangulations

The site percolation threshold for the random Voronoi network is determined numerically for the first time, with the result p_c = 0.71410 +/- 0.00002, using Monte-Carlo simulation on periodic systems of up to 40000 sites. The result is very close to the recent theoretical estimate p_c = 0.7151 of Neher, Mecke, and Wagner. For the bond threshold on the Voronoi network, we find p_c = 0.666931 +/- 0.000005, implying that for its dual, the Delaunay triangulation, p_c = 0.333069 +/- 0.000005. These results rule out the conjecture by Hsu and Huang that the bond thresholds are 2/3 and 1/3 respectivel…

Universality of continuous phase transitions on random Voronoi graphs

The Voronoi construction is ubiquitous across the natural sciences and engineering. In statistical mechanics, though, critical phenomena have so far been only investigated on the Delaunay triangulation, the dual of a Voronoi graph. In this paper we set to fill this gap by studying the two most prominent systems of classical statistical mechanics, the equilibrium spin-1/2 Ising model and the non-equilibrium contact process, on two-dimensional random Voronoi graphs. Particular motivation comes from the fact that these graphs have vertices of constant coordination number, making it possible to is…

非周期、拓扑及非关联无序下干净临界点稳定性的数值研究

Numerical Study of Stability of Clean Critical Points across Aperiodic, Topological, and Uncorrelated Disorder

本研究通过二维Ashkin-Teller模型数值比较三种非周期晶格的临界行为，发现稀释晶格破坏干净普适性，而Smith-hat平铺和VD三角剖分保持干净AT普适类，验证了HBV判据优于Harris判据。

具有不连续相变的可激发模型中的慢活动衰减

Slow activity decay in excitable models with discontinuous phase transitions

本研究通过阈值接触过程模型，发现可激发系统中存在由自发形成的缓慢消失活动簇引起的慢于指数的活动衰减，并指出该现象受晶格维数和小世界特性影响，且衰减稳定性依赖于幂律指数是否超过1/2。