Spectral Signatures of Third-Order Pseudo-Transitions in Finite Systems: An Eigen-Microstate Approach
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914498773778432 |
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| author | Liu, Wei Lv, Songzhi Zhang, Xin Wang, Fangfang Qi, Kai Di, Zengru |
| author_facet | Liu, Wei Lv, Songzhi Zhang, Xin Wang, Fangfang Qi, Kai Di, Zengru |
| contents | Third-order pseudo-transitions in finite systems reflect reorganization beyond conventional criticality, yet their identification usually relies on microcanonical entropy, which is often inaccessible in practice. Here we introduce a spectral generalized response within the eigen-microstate framework. From the distribution of normalized spectral weights, we construct the third-order ratio $R_3=K_3/(K_2)^3$, which probes asymmetric redistribution among fluctuation modes beyond leading-mode condensation. Across Ising and Potts models on regular lattices and random regular networks, extrema of $R_3$ consistently track higher-order anomalies. Combined with spectral projection, the method further distinguishes dependent and independent branches: the former remain tied to the dominant ordering channel, whereas the latter arise from redistribution within the subleading fluctuation subspace. The effective spectral dimension $R_{\mathrm{eff}}$ provides the participation background in which these anomalies develop. These results establish a geometric characterization of third-order pseudo-transitions as reorganizations of statistical weight in configuration space and provide an order-parameter-free route to finite-size structural criticality. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_19244 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral Signatures of Third-Order Pseudo-Transitions in Finite Systems: An Eigen-Microstate Approach Liu, Wei Lv, Songzhi Zhang, Xin Wang, Fangfang Qi, Kai Di, Zengru Statistical Mechanics Third-order pseudo-transitions in finite systems reflect reorganization beyond conventional criticality, yet their identification usually relies on microcanonical entropy, which is often inaccessible in practice. Here we introduce a spectral generalized response within the eigen-microstate framework. From the distribution of normalized spectral weights, we construct the third-order ratio $R_3=K_3/(K_2)^3$, which probes asymmetric redistribution among fluctuation modes beyond leading-mode condensation. Across Ising and Potts models on regular lattices and random regular networks, extrema of $R_3$ consistently track higher-order anomalies. Combined with spectral projection, the method further distinguishes dependent and independent branches: the former remain tied to the dominant ordering channel, whereas the latter arise from redistribution within the subleading fluctuation subspace. The effective spectral dimension $R_{\mathrm{eff}}$ provides the participation background in which these anomalies develop. These results establish a geometric characterization of third-order pseudo-transitions as reorganizations of statistical weight in configuration space and provide an order-parameter-free route to finite-size structural criticality. |
| title | Spectral Signatures of Third-Order Pseudo-Transitions in Finite Systems: An Eigen-Microstate Approach |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2604.19244 |