Detecting Multiple Phase Transitions in Lattice Systems with Intrinsic Dimensions
Abstract
Lattice systems with multiple nearby transitions pose two related challenges: resolving distinct transition scales and identifying the degrees of freedom primarily associated with each transition. We show that the intrinsic dimension of Monte Carlo configuration ensembles, estimated by the two-nearest-neighbors method, provides a geometric diagnostic for both problems. In the two-dimensional q-state clock model, the intrinsic dimension distinguishes the ordered, quasi-critical, and disordered regimes for both well-separated (q=9) and closely spaced (q=5) Berezinskii--Kosterlitz--Thouless transitions. In the q=5 case, the intermediate phase appears as a broad low-dimensional valley even when energy and magnetization do not separately resolve the two transitions. In the four-dimensional U(1) Higgs model, we introduce channel-decomposed intrinsic dimensions based on gauge-invariant plaquette and Higgs variables. The dominant response of each channel tracks transitions associated with the corresponding degrees of freedom, while the combined channel retains features of both. We further show that intrinsic dimensions evaluated directly on gauge-variant fields are dominated by gauge-orbit directions, demonstrating the importance of removing gauge redundancy before interpreting configuration-space geometry. These results establish channel-decomposed intrinsic dimension as a geometric probe of lattice systems with multiple transitions and motivate its application to disentangling deconfinement and chiral crossover scales in full QCD.
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BibTeX
@misc{mei2026detecting,
title = {{Detecting Multiple Phase Transitions in Lattice Systems with Intrinsic Dimensions}},
author = {Jie Mei and Tetsuo Hatsuda and Mei Huang and Lingxiao Wang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29090},
eprint = {2608.29090},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29090},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Detecting Multiple Phase Transitions in Lattice Systems with Intrinsic Dimensions
AU - Jie Mei
AU - Tetsuo Hatsuda
AU - Mei Huang
AU - Lingxiao Wang
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29090
UR - https://arxiv.org/abs/2608.29090
AB - Lattice systems with multiple nearby transitions pose two related challenges: resolving distinct transition scales and identifying the degrees of freedom primarily associated with each transition. We show that the intrinsic dimension of Monte Carlo configuration ensembles, estimated by the two-nearest-neighbors method, provides a geometric diagnostic for both problems. In the two-dimensional q-state clock model, the intrinsic dimension distinguishes the ordered, quasi-critical, and disordered regimes for both well-separated (q=9) and closely spaced (q=5) Berezinskii--Kosterlitz--Thouless transitions. In the q=5 case, the intermediate phase appears as a broad low-dimensional valley even when energy and magnetization do not separately resolve the two transitions. In the four-dimensional U(1) Higgs model, we introduce channel-decomposed intrinsic dimensions based on gauge-invariant plaquette and Higgs variables. The dominant response of each channel tracks transitions associated with the corresponding degrees of freedom, while the combined channel retains features of both. We further show that intrinsic dimensions evaluated directly on gauge-variant fields are dominated by gauge-orbit directions, demonstrating the importance of removing gauge redundancy before interpreting configuration-space geometry. These results establish channel-decomposed intrinsic dimension as a geometric probe of lattice systems with multiple transitions and motivate its application to disentangling deconfinement and chiral crossover scales in full QCD.
ER -