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Phase Transitions02:31

Phase Transitions

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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Phase Transitions01:21

Phase Transitions

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A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
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Phase Transitions: Sublimation and Deposition02:33

Phase Transitions: Sublimation and Deposition

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Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
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Phase Changes01:19

Phase Changes

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Phase transitions play an important theoretical and practical role in the study of heat flow. In melting or fusion, a solid turns into a liquid; the opposite process is freezing. In evaporation, a liquid turns into a gas; the opposite process is condensation.
A substance melts or freezes at a temperature called its melting point and boils or condenses at its boiling point. These temperatures depend on pressure. High pressure favors the denser form of the substance, so typically, high pressure...
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Phase Transitions: Vaporization and Condensation02:39

Phase Transitions: Vaporization and Condensation

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The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase...
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Phase Diagram01:19

Phase Diagram

5.9K
The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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Using Generative Art to Convey Past and Future Climate Transitions
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Detecting Phase Transitions from Data Using Generative Learning.

Xiyu Zhou1,2,3, Yan Mi2,3, Pan Zhang1,3

  • 1School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China.

Entropy (Basel, Switzerland)
|May 4, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a data-driven framework using machine learning to detect phase transitions in complex systems directly from raw data, bypassing the need for predefined models or parameters.

Keywords:
generative learningmachine-learningphase transitionvariational autoregressive networks

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Area of Science:

  • Statistical Physics
  • Machine Learning
  • Complex Systems

Background:

  • Traditional phase transition identification requires order parameters and model knowledge.
  • This often necessitates understanding the underlying statistical model and symmetry-breaking mechanisms.
  • A data-driven approach is needed for systems lacking complete theoretical descriptions.

Purpose of the Study:

  • To develop a novel framework for detecting phase transitions directly from raw experimental data.
  • To eliminate the need for prior knowledge of model Hamiltonians, parameters, or labels.
  • To provide a general, data-driven tool for exploring critical phenomena.

Main Methods:

  • Utilized autoregressive neural networks (a type of generative model) to estimate the system's probability distribution from raw configuration data.
  • Quantified the sensitivity of the learned distribution to control parameters (e.g., temperature).
  • Developed a phase transition indicator based on the expectation of change in absolute logarithmic probability.

Main Results:

  • The generative framework accurately identified phase transitions in the 2D Ising model (triangular and square lattices) and the Sherrington-Kirkpatrick model.
  • Validation used raw data from Markov Chain Monte Carlo and Tensor Network methods.
  • The approach successfully detected transitions using only raw data, demonstrating its purely data-driven nature.

Conclusions:

  • The proposed framework offers a robust, data-driven method for identifying phase transitions without prior model information.
  • This approach is broadly applicable to various complex systems and critical phenomena.
  • Potential for extension to analyze realistic experimental data where theoretical models are incomplete.