arXiv subjects

Huiseung Chae

Publications and source records attributed to Huiseung Chae.

3 recordsLinked to original sources

arXiv2013

Phase transitions in Paradigm models

In this letter we propose two general models for paradigm shift, deterministic propagation model (DM) and stochastic propagation model (SM). By defining the order parameter $m$ based on the diversity of ideas, $Δ$, we study when and how the transition occurs as a cost $C$ in DM or an innovation probability $α$ in SM increases. In addition, we also investigate how the propagation processes affect on the transition nature. From the analytical calculations and numerical simulations $m$ is shown to satisfy the scaling relation $m=1-f(C/N)$ for DM with the number of agents $N$. In contrast, $m$ in SM scales as $m=1-f(α^a N)$.

physics.soc-ph↗

arXiv2012

Agglomerative percolation on the Bethe lattice and the triangular cactus

We study the agglomerative percolation (AP) models on the Bethe lattice and the triangular cactus to establish the exact mean-field theory for AP. Using the self-consistent simulation method, based on the exact self-consistent equation, we directly measure the order parameter $P_{\infty}$ and average cluster size $S$. From the measured $P_{\infty}$ and $S$ we obtain the critical exponents $β_k$ and $γ_k$ for $k=2$ and 3. Here $β_k$ and $γ_k$ are the critical exponents for $P_\infty$ and $S$ when the growth of clusters spontaneously breaks the $Z_k$ symmetry of the $k$-partite graph (Lau, Paczuski, and Grassberger, 2012). The obtained values are $β_2=1.79(3)$, $γ_2=0.88(1)$, $β_3=1.35(5)$, and $γ_3=0.94(2)$. By comparing these values of exponents with those for ordinary percolation ($β_{\infty}=1$ and $γ_{\infty}=1$) we also find the inequalities between the exponents, as $β_\infty<β_3<β_2$ and $γ_\infty>γ_3>γ_2$. These results quantitatively verify the conjecture that the AP model belongs to a new universality class if $Z_k$ symmetry is broken spontaneously, and the new universality class depends on $k$ [Lau et al., Phys. Rev. E 86, 011118 (2012)].

cond-mat.stat-mech↗

arXiv2012

Explosive percolations on the Bethe Lattice

Based on the self-consistent equations of the order parameter $P_\infty$ and the mean cluster size $S$, we develop a novel self-consistent simulation (SCS) method for arbitrary percolation on the Bethe lattice (infinite homogeneous Cayley tree). By applying SCS to the well-known percolation models, random bond percolation and bootstrap percolation, we obtain prototype functions for continuous and discontinuous phase transitions. By comparing the key functions obtained from SCSs for the Achlioptas processes (APs) with a product rule and a sum rule to the prototype functions, we show that the percolation transition of AP models on the Bethe lattice is continuous regardless of details of growth rules.

cond-mat.stat-mech↗