市场晶体：集体加密货币状态的自旋晶格模型
The Market Crystal: A Spin-Lattice Model for Collective Cryptocurrency States
AI总结：
受多体系统类比启发，提出自旋晶格模型将加密货币资产编码为二元自旋变量，通过相关广度优先搜索嵌入169种加密货币到13×13晶格，构建伊辛类哈密顿量（市场晶体），用磁化强度和能量等宏观可观测量表征集体市场状态，揭示铁磁相互作用主导的相空间结构。
摘要：
金融市场中的集体动力学可以通过大量资产的同步运动而涌现。受相互作用多体系统类比的启发，我们引入了一个自旋晶格表示来分析加密货币市场中的集体状态。在该框架中，根据资产收益的符号将资产编码为二元自旋变量，而资产之间的相关性决定了有效相互作用强度。基于相关性的广度优先搜索（CBFS）过程将169种加密货币嵌入到一个$13 \ imes 13$的晶格中，从而能够构建一个描述市场配置的伊辛类哈密顿量，我们称之为\emph{市场晶体}。宏观可观测量如磁化强度和能量提供了集体市场状态的统计力学表征。由此产生的相空间结构突出了资产之间强对齐和碎片化的状态，其能量-磁化强度模式暗示了以铁磁相互作用为主。该框架为研究金融系统中的集体行为提供了统计力学视角。
英文摘要：
Collective dynamics in financial markets can emerge through synchronized movements of large groups of assets. Motivated by analogies with interacting many-body systems, we introduce a spin-lattice representation for analyzing collective states in cryptocurrency markets. In this framework, assets are encoded as binary spin variables according to the sign of their returns, while correlations between assets determine effective interaction strengths. A correlation-based breadth-first search (CBFS) procedure embeds 169 cryptocurrencies into a $13 \times 13$ lattice, enabling the construction of an Ising-like Hamiltonian describing the market configuration, which we call the \emph{Market Crystal}. Macroscopic observables such as magnetization and energy provide a statistical-mechanical characterization of collective market states. The resulting phase-space structure highlights regimes of strong alignment and fragmentation among assets, with an energy--magnetization pattern suggestive of predominantly ferromagnetic interactions. This framework offers a statistical-mechanical viewpoint for studying collective behavior in financial systems.
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