随机耦合场中的临界性质与玻璃化转变
Critical Properties and Glass Transitions in Randomly Coupled Fields
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中文总结 AI 辅助
研究随机耦合的N个标量场集合，通过Wigner矩阵与球形变体模型分析其临界性质，发现上临界维度为1，d>1时热容跃变且玻璃相具标度不变性。
中文摘要 AI 辅助
我们研究了由淬火随机相互作用耦合的N个标量场的集合，这等价于自旋玻璃，其自旋被提升为d维场。当N很大时，随机耦合矩阵会产生一系列高斯普适类，其临界指数由谱边缘附近的本征值密度行为决定。对于Wigner矩阵，关联长度在临界点发散，但 susceptibility（ susceptibility：磁化率，保留英文原名）保持有限，单圈副本分析支持上临界维度为1。在可精确求解的球形变体中，当d>1时，热容在转变处发生跃变，且在整个玻璃相中，关联保持其临界形式，尽管无Goldstone模式，仍呈现出普适的标度不变性。
英文摘要
We study an assembly of $N$ scalar fields coupled via a quenched random interaction, equivalent to a spin glass whose spins are promoted to $d$-dimensional fields. When $N$ is large, the random coupling matrix produces a family of Gaussian universality classes whose critical exponents are determined by the behavior of the eigenvalue density near the spectral edge. For a Wigner matrix, the correlation length diverges at criticality but the susceptibility remains finite, and one-loop replica analysis supports an upper critical dimension of unity. In an exactly solvable spherical variant, the heat capacity jumps at the transition in $d>1$, and correlations remain pinned to their critical form throughout the glass phase, giving generic scale invariance despite the absence of a Goldstone mode.
