# Do spatially non-uniform phases of matter with no long-range order exist?

@article{Tth2020DoSN, title={Do spatially non-uniform phases of matter with no long-range order exist?}, author={Gyula I. T{\'o}th}, journal={arXiv: Statistical Mechanics}, year={2020} }

In this Letter, the existence of spatially non-uniform phases with no long-range order is investigated in continuum models of first order phase transitions with quartic non-linearity. The central result of the paper is the development of a mathematical method allowing to find "disordered" solutions (infinite sets of spatially non-uniform analytical solutions with no long range order) to partial differential equations. The new method is applied for the Gaussian measure, and it has been found…

## References

SHOWING 1-10 OF 26 REFERENCES

### Theory of structural glasses and supercooled liquids.

- PhysicsAnnual review of physical chemistry
- 2007

We review the random first-order transition theory of the glass transition, emphasizing the experimental tests of the theory. Many distinct phenomena are quantitatively predicted or explained by the…

### Derivation of the Time-Dependent Ginzburg-Landau Equation on the Line

- Mathematics
- 1998

Summary. We give a rigorous derivation of the time-dependent one-dimensional Ginzburg—Landau equation. As in the work of Iooss, Mielke, and Demay [11] (who derived the steady Ginzburg-Landau…

### On radial solutions of the Swift-Hohenberg equation

- Mathematics, Physics
- 2008

We study radial solutions to the generalized Swift-Hohenberg equation on the plane with an additional quadratic term. We find stationary localized radial solutions that decay at infinity and…

### Highly ordered noncrystalline metallic phase.

- Materials SciencePhysical review letters
- 2013

We report the characterization of a unique metallic glass that, during rapid cooling of an Al-Fe-Si melt, forms by nucleation, followed by growth normal to a moving interface between the solid and…

### Spots in the Swift-Hohenberg Equation

- MathematicsSIAM J. Appl. Dyn. Syst.
- 2013

The existence of stationary localized spots for the planar and the three-dimensional Swift--Hohenberg equations is proved using geometric blow-up techniques. The spots found in this paper have a much…

### Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of Thermodynamics

- Chemistry
- 1902

Preface 1. General notions. The principle of conservation of extension-in-phase 2. Application of the principle of conservation of extension-in-phase to the theory of errors 3. Application of the…

### High density amorphous ice at room temperature

- Materials ScienceProceedings of the National Academy of Sciences
- 2011

High density amorphous (HDA) ice is formed from metastable ice VII in the stability field of ice VI under rapid compression using dynamic-diamond anvil cell (d-DAC) and results from structural similarities between HDA and ice VII, indicating that structural instabilities of parent ice VII and Ih drive the pressure-induced amorphization.

### Modeling elasticity in crystal growth.

- Materials SciencePhysical review letters
- 2002

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales in a natural manner and enables access to time scales much larger than conventional atomic methods.

### Concentration of measure and isoperimetric inequalities in product spaces

- Mathematics
- 1994

The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product ΩN of probability spaces has measure at least one half, “most” of the points of Ωn are “close”…