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Phase Transitions

Phase Transitions

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...

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...

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...

Phase Diagram

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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).

Phase Transitions: Melting and Freezing

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...

Phase Diagrams

Phase Diagrams

A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...

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Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions

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Published on: April 19, 2018

Describing self-organized criticality as a continuous phase transition.

¹B-1/16 East Enclave Housing, 02 Biswa Bangla Sarani, New Town, Kolkata 700163, India.

Physical Review. E

|March 19, 2025

Summary

Self-organized criticality, like sandpile models, can be described as continuous phase transitions. Numerical evidence shows tuning drop density reveals critical phases and scaling behaviors.

Area of Science:

Complex Systems
Statistical Physics

Background:

Self-organized criticality (SOC) describes systems naturally evolving to critical states.
Sandpile models, like Bak-Tang-Wiesenfeld (BTW) and Manna, are key examples of SOC.
Understanding SOC within continuous phase transition frameworks is an open question.

Purpose of the Study:

To investigate if self-organized criticality (SOC) phenomena, using sandpile models, can be framed as continuous phase transitions.
To explore the relationship between percolation transitions and SOC.
To identify and analyze order parameters and critical exponents for SOC.

Main Methods:

Numerical simulations of the Bak, Tang, and Wiesenfeld (BTW) and Manna sandpile models.
Introduction and manipulation of 'drop density' as a control parameter.

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Analysis of avalanche size distribution and scaling behavior.

Calculation of the correlation length exponent.

Main Results:

Extensive numerical evidence supports that SOC can be described by continuous phase transitions.
Tuning the drop density reveals a transition from subcritical to critical phases in sandpiles.
The scaled size of the largest avalanche serves as an effective order parameter.
The correlation length exponent diverges at the critical point, consistent with phase transitions.

Conclusions:

Sandpile models exhibit characteristics of continuous phase transitions.
The concept of drop density provides a means to tune SOC systems across critical points.
SOC systems share universality classes with other continuous phase transitions.