Continuously magnifying a crystal reveals highly ordered atoms; But when you zoom in on a piece of glass, you will see a relatively chaotic picture, like a random plate of scattered sand.

Mathematically, highly ordered crystals are easier to understand, and physicists have long developed a range of theories to describe the properties of crystals—from how they absorb heat to what they do after they break. But for amorphous or disordered materials such as glass, frozen food or certain plastics, there is currently no generally accepted theory that explains their physical behavior.

 For the past 30 years, physicists have been debating whether a mysterious phase transition that exists in the theoretical models of these disordered materials also exists in real life glass. Drawing on some mathematical magic borrowed from particle physics, coupled with dozens of pages of handwritten algebraic calculations, Duke University researcher Sho Yaida finally resolved this debate that has lasted for nearly 30 years.

Through a 30 page manual calculation, Sho Yaida revealed the mysterious essence of glass and other disordered materials at low temperatures. They are likely to be a completely new state of matter.

 Yaida's insight has opened up the possibility that certain types of glass can be in a new material state at low temperatures. This means that at low temperatures, glass may react differently to heat, sound, and pressure.

 Patrick Charbonneau, the mentor of Sho Yaida, said, "We have found clues to this phase transition, but previously we dared not say that this is evidence of this phase transition because the academic community generally believed it to be impossible. Sho has proven that it can exist.”

 But what surprised Charbonneau the most was that the mathematics behind glass and other disordered systems were easier to solve in the hypothetical infinite dimensional universe. In infinite dimensions, their properties can be relatively easily calculated, similar to calculating the properties of crystals in a three-dimensional universe.

 A characteristic of these infinite dimensional calculations is the existence of a phase transition, known as the "Gadner phase transition". If this phase transition exists in glass, it will significantly change the properties of the glass at low temperatures.

But does this phase transition that clearly exists in infinite dimensions also exist in three dimensions? Back in the 1980s, a group of physicists conducted mathematical calculations and provided a negative answer. Therefore, in the past 30 years, the general view in the physics community has been that although this phase transition is theoretically interesting, it is not related to the real world.

 Until recently, Charbonneau and others discovered clues to the presence of this phase transition on three-dimensional glass in experiments and simulations of glass formation.

Yaida, with a background in particle physics, has re studied past mathematical proofs. He found that previous calculations did not find a "fixed point" in three-dimensional space - this is a prerequisite for the existence of this phase transition. He believes that with further calculation, he may get a different answer.

In expired calculations, researchers are unable to find a "fixed point" in 3D, or a point where all lines overlap. Through further calculations, Yaida determined the position of this point, proving that there may be a new phase transition in the glass at low temperatures.

After a month of hard work and a 30 page calculation manuscript, Yaida finally proved her guess. Yaida said, "This moment is precisely why I am committed to science. Although it is only a small point, it is of great significance to researchers in this field. It has enabled the strange states of matter that people struggled to pursue in the 1970s and 1980s to have physical connections in the three-dimensional world.

After a year of repeated proofreading and dozens of additional pages of auxiliary calculations, this result was finally published in the Physics Review Letters on May 26th. 

"The fact that this phase transition may be real in the three-dimensional world means we should start taking it seriously," Charbonneau said. "It affects how sound travels, how much heat is absorbed, how information is transmitted. And if shearing starts. Glass, how it will form, how it will break. This research has profound implications for our understanding of amorphous crystals, whether they are plastic, loose sand or glass."