定向聚合物玻璃的谱学研究途径
A Spectral Route to Directed-Polymer Glasses
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中文总结 AI 辅助
本研究针对定向聚合物玻璃模型，通过将问题转化为填充单聚合物转移矩阵乘积的对数本征值，获得了与复制理论预测一致的结果，为该模型的数值检验提供了新的谱学途径。
中文摘要 AI 辅助
淬火随机介质中有限密度的相互回避定向聚合物是玻璃态线性物质的最小模型。通过复制贝叶斯 ansatz 求解的稀溶液理论预测，相互作用自由能与密度ρ²成正比，无序累积量对密度ρ呈现不同的幂律依赖关系，但组合上庞大的多聚合物转移矩阵阻碍了直接数值检验。我们将该问题重铸为填充单聚合物转移矩阵乘积的对数本征值，得到了淬火自由能、其累积量以及与复制预测一致的无序诱导线性谱边。
英文摘要
A finite density of mutually avoiding directed polymers in a quenched random medium is a minimal model of glassy line matter. The dilute theory, solved by replica Bethe ansatz, predicts an interaction free energy proportional to $ρ^2$ and disorder cumulants with distinct power-law dependences on the density $ρ$, but direct numerical tests have been hindered by the combinatorially large many-polymer transfer matrix. We recast the problem as filling logarithmic eigenvalues of a single-polymer transfer-matrix product, obtaining the quenched free energy, its cumulants, and a disorder-induced linear spectral edge consistent with the replica prediction.
