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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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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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The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
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Phase Transitions: Melting and Freezing02:39

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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...
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Phase Transitions: Sublimation and Deposition02:33

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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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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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Mixed-order phase transition in a one-dimensional model.

Amir Bar1, David Mukamel1

  • 1Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel.

Physical Review Letters
|February 4, 2014
PubMed
Summary
This summary is machine-generated.

We present a soluble one-dimensional Ising model demonstrating a mixed-order phase transition. This model links spin and depinning models, advancing a unifying framework for complex systems.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Mixed-order transitions, characterized by discontinuous order parameters and diverging correlation lengths, appear in diverse physical models.
  • Existing models exhibiting these transitions often seem unrelated, hindering a unified understanding.

Purpose of the Study:

  • Introduce and analyze a novel, exactly soluble one-dimensional Ising model.
  • Establish a connection between different classes of models exhibiting mixed-order transitions.

Main Methods:

  • Development of an exactly soluble one-dimensional Ising model with long-range interactions.
  • Analysis of the model's phase transition behavior, focusing on order parameter and correlation length.

Main Results:

  • The model exhibits a mixed-order phase transition.
  • The interaction's decay follows an inverse distance squared, linking it to specific spin models.
  • The model provides a bridge to depinning transition models.

Conclusions:

  • The presented Ising model offers a tractable framework for studying mixed-order transitions.
  • This work contributes to a unifying theoretical framework for phenomena across different physical systems.