PhaseTransition (PT) Dataset Overview

• PhaseTransition (PT) Dataset is a curated collection that records order parameters, microscopic configurations, and statistical descriptors to capture phase transitions.
• It integrates high-throughput simulations, experimental measurements, and machine learning models for automated feature extraction and unsupervised classification.
• The dataset supports reproducible phase diagram generation and benchmarking across a variety of physical, chemical, and biological systems.

The PhaseTransition (PT) Dataset refers to both curated data collections and methodological frameworks designed to characterize, detect, and analyze phase transitions in a wide variety of physical, chemical, biological, and artificial systems. The foundational purpose of these datasets is to facilitate the paper of abrupt or continuous changes in the qualitative behavior of a system’s macroscopic observables, often relating to symmetry breaking, free energy landscape evolution, or topological order. PT datasets integrate data from theoretical models, high-precision numerical simulations, experimental measurements, and machine learning–aided classifications, supporting reproducible discovery and benchmarking of phase transitions across scientific disciplines.

1. Definitions and Characteristic Content

PT datasets are constructed to systematically record and annotate data pertinent to phase transition phenomena under varied external conditions—temperature, pressure, external fields, disorder, or system size. Content typically includes:

• Order parameters and observable time series: e.g., spontaneous magnetization, polarization, density, entanglement entropy.
• Microscopic configurations: e.g., spin/lattice states, polarization fields, quantum many-body wavefunctions.
• Statistical descriptors: distributions of observables, persistence diagrams, correlation functions, autocorrelation decay profiles.
• Control parameters and associated phase diagrams: mappings between tunable system parameters (temperature, chemical potential, strain, applied field) and resultant phases.
• Spectral properties: eigenvalues and eigenvectors from (non-)Hermitian Hamiltonians, transmission/reflection spectra for photonic/phononic/metamaterial systems.

PT datasets may originate from:

• High-throughput simulations (e.g., time-dependent Ginzburg–Landau modeling for ferroelectrics (Du et al., 6 Apr 2025)).
• Experimental measurements with parameter sweeps (e.g., microwave metamaterial transmission through exceptional points (Li et al., 9 Apr 2024)).
• Automated data pipelines integrating machine learning for feature extraction, clustering, and anomaly detection.

2. Data Generation, Annotation, and Retrieval Strategies

PT dataset generation involves systematic sweeps of physical parameters and recording the system’s response. For example, in the domain of ferroelectric topological phases (Du et al., 6 Apr 2025), phase-field simulations are run over grids of layer thickness, lattice mismatch, substrate strain, and applied voltage, producing 3D polarization fields $P(\mathbf{r})$ for each parameter point. Nonstandard datasets supplement these with user-submitted or experimentally obtained 2D/3D domain structures.

Annotation typically leverages domain-specific statistical or computational geometry pipelines:

• Global Local Transformer (GL Transformer) frameworks extract hierarchical spatial features by dividing spatial cubes into sub-blocks, embedding polarization data, and clustering into topological categories (e.g., vortices, skyrmions, flux closures) (Du et al., 6 Apr 2025).
• Feature vectors from deep learning models (e.g., ResNet) are used for matching experimental images against simulation libraries, using similarity metrics such as cosine similarity on normalized feature vectors.
• Persistent homology or topological persistence analysis converts batches of configurations or raw correlation matrices into barcodes or persistence diagrams. Discrete topological events (birth/death of connectivity or cycles) are then tracked over tuning parameters to flag phase transitions (Donato et al., 2016, Tran et al., 2020).

Retrieval is supported via parameter-based queries (users specify values like substrate strain, voltage, or superlattice thickness to retrieve corresponding dataset slices) and image-based search (upload of microscopy images triggers a best-match retrieval against the simulated dataset).

3. Machine Learning and Topological Analysis Integration

State-of-the-art PT datasets tightly integrate machine learning and topological data analysis to automate and generalize detection, classification, and phase diagram generation:

• Transformer models serve as both feature extractors and classifiers, learning representations insensitive to global rotations or symmetries while remaining sensitive to local order or defects.
• Clustering algorithms (e.g., Ward linkage, spectral clustering with topological kernels) are employed to assign samples to phase or domain classes directly from learned feature embeddings.
• Persistent homology, filtration, and entropy features quantify the multi-scale structure and complexity of sampled configurations, providing powerful phase-sensitive signatures even in systems lacking conventional order parameters (Donato et al., 2016, Tran et al., 2020).
• Dimensionality reduction (e.g., UMAP, principal component analysis) and similarity metrics allow unsupervised delineation of phase boundaries and identification of crossover regions.

Unsupervised learning enables detection of phase transitions without requiring labeled data, a significant advantage in exploring systems where phase boundaries are a priori unknown or where the relevant order parameters are subtle or topological in nature.

4. Application Examples and Benchmark Models

Representative PT datasets have been developed and exploited in:

• Ferroelectric oxide superlattices: Cataloguing vortex, skyrmion, flux closure, and labyrinthine phases in 3D polarization fields as a function of composition, strain, and field (Du et al., 6 Apr 2025).
• Magnetic and electronic systems: Simulation-driven databases documenting transitions such as the Berezinskii–Kosterlitz–Thouless (BKT) transition in the XY model, Mott or topological transitions in correlated electron systems, with topological persistence descriptors as invariants (Tran et al., 2020).
• Non-Hermitian photonic structures and metamaterials: Recording of spectral, modal, and transmission properties of PT- and anti-PT-symmetric systems as control parameters (e.g., gain/loss balance, coupling phase, resonator frequency, dissipation) are swept through symmetry-breaking points (Li et al., 9 Apr 2024, Zhang et al., 2022).
• Quantum/classical simulation benchmarks: PT datasets have been used to validate enhanced sampling strategies (e.g., parallel vs. simulated tempering) for efficiently equilibrating near first- or second-order transitions (Fiore et al., 2010).
• Economic and biological systems: Recordings of volatility, skewness, autocorrelations, and scaling exponents around critical events (e.g., market crashes as dynamic phase transitions), assembled for predictive analytics based on phase transition theory (Nayar et al., 12 Aug 2024).

5. Phase Diagram Construction and Visualization

PT datasets commonly support phase diagram generation by mapping empirical or inferred phase labels onto a regularly spaced grid in parameter space. Notable methodologies include:

• Binary and multi-class phase diagram generators: Classification outputs (e.g., from GL-Transformer) populate a 2D or 3D parameter grid, producing color-coded phase maps indicating domain topologies, transition boundaries, and phase coexistence regions (Du et al., 6 Apr 2025).
• Interactive tools: Users select parameter axes and ranges (e.g., applied field, substrate lattice parameter), with phase diagrams rendered on the fly.
• Integration of topological and ML features: Persistent homology or clustering boundaries serve as the operational definition of phase transitions, particularly where scalar order parameters are absent or insufficient (Tran et al., 2020, Donato et al., 2016).
• Benchmarking and reproducibility: Standard datasets supply ready-to-use polarization maps or configuration initializations, reducing the need for time-consuming phase field relaxation in repeated studies.

6. Data Accessibility, Community Contribution, and Impact

Modern PT Datasets emphasize open access and reproducibility:

• Web interfaces facilitate search by parameter sweep or similarity queries, direct download of simulation data, and visualization of polarization configurations or domain structures (Du et al., 6 Apr 2025).
• Community-driven submission: Nonstandard datasets collected from user uploads (either experimental or computational) enable continual expansion and diversification of the repository.
• Bridging experiment and simulation: The integration of image-based retrieval allows experimentalists to identify theoretically analogous structures and benchmark data-driven phase diagrams.
• Reduction of computational and experimental redundancy: By standardizing initial conditions, facilitating rapid model validation, and lowering technical barriers, PT Datasets streamline collaborative science.

The increasing sophistication of PT Datasets—via machine learning, topological data analysis, and hybrid simulation–experimental workflows—promotes the rapid, reproducible mapping of phase diagrams, deeper insight into domain morphologies, and cross-validation of theoretical, numerical, and empirical phase transition research.

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Table: Key Components of a Modern PhaseTransition Dataset

Component	Example Techniques	Physical Systems
Simulation and Experiment	Phase field methods, spectroscopy, microscopy	Ferroelectrics, photonics, quantum materials
Feature Extraction	Transformers, persistent homology, clustering	XY, Ising, Bose-Hubbard models
Phase Diagram Generation	Binary/multiclass mapping, ML-aided labeling	Topological, magnetic, electronic transitions
Accessibility & Search	Web, API, image-based retrieval	User-driven, cross-domain
Community Contribution	Uploads, curation, reproducibility tools	Experimental/theoretical synergy