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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...

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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 Transitions: Vaporization and Condensation

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Chirality

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Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
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Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3–12 are transition elements. The f-block elements, also called inner transition metals (the lanthanides and actinides), also meet this criterion because the d orbital is partially occupied before the f orbitals.

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Related Experiment Video

Updated: Jan 26, 2026

A Micropatterning Assay for Measuring Cell Chirality

A Micropatterning Assay for Measuring Cell Chirality

Published on: March 11, 2022

Floating Phase versus Chiral Transition in a 1D Hard-Boson Model.

Natalia Chepiga¹, Frédéric Mila²

¹Department of Physics and Astronomy, University of California, Irvine, California 92697, USA.

Physical Review Letters

|April 24, 2019

Summary

Researchers studied a hard-boson model phase transition using advanced algorithms. They found evidence for an intermediate floating phase and a unique transition in the Huse-Fisher chiral universality class.

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Area of Science:

Condensed Matter Physics
Quantum Simulation

Background:

Hard-boson models are crucial for understanding quantum phenomena in cold-atom experiments.
Phase transitions in these systems are complex and require accurate theoretical and numerical investigation.

Purpose of the Study:

To investigate the phase transition between the period-three charge-density wave and the disordered phase in a hard-boson model.
To accurately determine critical properties and universality classes of the transition.

Main Methods:

Utilized a density-matrix renormalization group (DMRG) algorithm optimized for hard-boson constraints.
Studied large systems up to 9000 sites.
Calculated correlation length and wave vector of incommensurate correlations with high precision.

Main Results:

Provided strong numerical evidence for an intermediate floating phase away from the integrable Potts point.
Observed that near the integrable Potts point, the transition aligns with the Huse-Fisher chiral universality class.

Conclusions:

The hard-boson model exhibits a rich phase diagram with distinct critical behaviors.
Numerical findings confirm the presence of a floating phase and identify the universality class of the transition in specific regimes.