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Related Concept Videos

Phase Transitions02:31

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 occupy...
Phase Transitions01:21

Phase Transitions

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...
Phase Diagram01:19

Phase Diagram

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 Diagram01:24

Phase Diagram

A phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. It shows the boundaries between solid, liquid, and gas phases and the conditions at which these phases coexist in equilibrium. An area in a phase diagram represents a single phase, whereas lines or phase boundaries represent the equilibrium between two phases.In the phase diagram of water, the boundary line between the solid and liquid states illustrates...
Phase Transitions: Sublimation and Deposition02:33

Phase Transitions: Sublimation and Deposition

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...
The Phase Rule01:20

The Phase Rule

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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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
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Second-order phase transition in causal dynamical triangulations.

Jan Ambjørn1, S Jordan, J Jurkiewicz

  • 1The Niels Bohr Institute, Copenhagen University, Denmark. ambjorn@nbi.dk

Physical Review Letters
|December 21, 2011
PubMed
Summary
This summary is machine-generated.

Causal dynamical triangulations offer a nonperturbative path integral for quantum gravity. Evidence suggests a second-order phase transition, enabling a continuum limit for quantum gravity theories.

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Area of Science:

  • Theoretical physics
  • Quantum gravity
  • String theory

Background:

  • Causal dynamical triangulations (CDT) provide a framework for defining quantum gravity.
  • A key challenge is establishing a continuum limit for quantum gravity theories.

Purpose of the Study:

  • To investigate the phase structure of lattice quantum gravity using CDT.
  • To identify conditions for defining a continuum limit in quantum gravity.

Main Methods:

  • Utilizing causal dynamical triangulations as a nonperturbative approach.
  • Analyzing the lattice theory for phase transitions.

Main Results:

  • Strong evidence for a second-order phase transition line in the lattice theory.
  • The identified transition line offers a potential route to a continuum limit.

Conclusions:

  • The findings support CDT as a viable approach to quantum gravity.
  • A second-order phase transition is crucial for defining a continuum limit in quantum gravity research.