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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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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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Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression...
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Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...
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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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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...
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Geometric critical exponents in classical and quantum phase transitions.

Prashant Kumar1, Tapobrata Sarkar1

  • 1Department of Physics, Indian Institute of Technology, Kanpur 208016, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 7, 2014
PubMed
Summary
This summary is machine-generated.

We introduce geometric critical exponents for classical and quantum phase transitions. These exponents, calculated analytically, appear universal across both system types, offering new insights into critical phenomena.

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Area of Science:

  • Theoretical Physics
  • Condensed Matter Physics
  • Quantum Information Theory

Background:

  • Continuous second-order phase transitions are fundamental in both classical and quantum systems.
  • Understanding critical phenomena requires characterizing system behavior near transition points.
  • Information-theoretic approaches offer novel perspectives on phase transitions.

Purpose of the Study:

  • To define and calculate novel geometric critical exponents for continuous second-order classical and quantum phase transitions.
  • To investigate the relationship between geometric properties of parameter manifolds and critical behavior.
  • To explore the universality of these geometric critical exponents.

Main Methods:

  • Definition of geometric critical exponents based on scalar quantities on information-theoretic parameter manifolds.
  • Analytical calculation of exponents by approximating the metric near curvature singularities.
  • Solving geodesic equations in two-dimensional parameter manifolds.

Main Results:

  • Geometric critical exponents are defined for classical and quantum phase transitions.
  • Exponents are calculated analytically by approximating the metric and solving geodesic equations.
  • The calculated critical exponents are identical for both classical and quantum systems studied.

Conclusions:

  • The geometric critical exponents are the same for both classical and quantum systems.
  • Evidence suggests potential universality of these geometric critical exponents.
  • This work provides a new geometric framework for understanding critical phenomena.