重新审视连续性状阿克塞尔罗德模型的非平衡相变
Revisiting the non-equilibrium phase transitions of the continuous-trait Axelrod model
浏览论文内容
中文总结 AI 辅助
研究连续性状阿克塞尔罗德模型的非平衡相变，通过分析中位数缩放和概率分布揭示其相变特征，发现\(F = 2\)时为混合转变，\(F = 3\)时为非混合一阶转变，还应用于离散泊松变体建立统一表征。
中文摘要 AI 辅助
我们研究连续性状阿克塞尔罗德模型的非平衡相变，该模型中个体文化由\(F\)个连续特征向量表示，局限于区间\((0,1)\)。局部相互作用由度量相似性阈值\(d\)控制，\(d\)作为社会容忍度的连续控制参数。动力学不可避免地冻结为两种吸收配置类之一：高容忍度下的有序、同质单文化状态，或低容忍度下的高度碎片化、无序状态。先前研究基于域密度\(\mu\)的连续行为以及最大域分数\(\rho\)的不连续跳跃将转变表征为混合转变，我们表明这种明显的连续性是严重有限尺寸掩盖效应的假象。通过将方法重点转移到中位数\(\tilde{\mu}\)的缩放并分析完整概率分布\(P(\mu)\)，我们揭示了在独立模拟运行中具有不相交最大值的清晰双峰结构。我们的结果表明，对于\(F = 2\)，系统经历当代意义上真正的混合转变，在临界阈值\(d_c \approx 0.0784\)处具有微小但有限的潜在跳跃\((\mu_c \approx 0.089)\)，同时从下方通过具有平均场指数\(\beta \approx 1/2\)的非解析幂律向其缩放。相反，对于\(F = 3\)，更高的性状空间维度抑制局部波动，产生传统的、非混合的一阶转变。我们将此框架应用于模型的替代离散泊松变体，成功确认了其已知的\(F = 2\)时的连续转变和\(F = 3\)时的不连续、非混合转变，从而建立了阿克塞尔罗德类系统相变的统一表征。
英文摘要
We investigate the non-equilibrium phase transitions of the continuous-trait Axelrod model, an agent-based framework where individual culture is represented by a vector of $F$ continuous features confined to the interval $(0,1)$. Local interactions are governed by a metric similarity threshold $d$, which acts as a continuous control parameter of social tolerance. The dynamics inevitably freeze into one of two absorbing configuration classes: an ordered, homogeneous monocultural state at high tolerance, or a highly fragmented, disordered state at low tolerance. While previous studies characterized the transition as hybrid based on the continuous behavior of the domain density $μ$ alongside a discontinuous jump in the largest domain fraction $ρ$, we show that this apparent continuity is an artifact of severe finite-size masking effects. By shifting the methodological focus to the scaling of the median $\tildeμ$ and analyzing the full probability distributions $P(μ)$, we unveil a clear bimodal structure with disjoint maxima across independent simulation runs. Our results reveal that for $F=2$, the system undergoes a genuinely hybrid transition in the contemporary sense, featuring a tiny but finite latent jump ($μ_c \approx 0.089$) at the critical threshold $d_c \approx 0.0784$ while scaling toward it from below via a non-analytical power law with a mean-field exponent $β\approx 1/2$. Conversely, for $F=3$, the higher trait-space dimensionality suppresses local fluctuations, yielding a traditional, non-hybrid first-order transition. We apply this framework to the alternative discrete Poisson variant of the model, successfully confirming its known continuous transition for $F=2$ and discontinuous, non-hybrid transition for $F=3$, thereby establishing a unified characterization of phase transitions in Axelrod-like systems.
