quantum ising model

Two dancers on one stage: one pulls the partner in one direction, the other in the opposite. In the crystal Cu2(OH)3Br, known as botallackite, copper atoms form chains where the spins (magnetic moments) of neighboring ions align either parallel, as in a ferromagnet, or antiparallel, as in an antiferromagnet.

A quantum computer is usually like an assembly line: operations proceed one after another, and each error accumulates. In the new work, physicists tried a different path — an architecture where the computation grows out of the measurement process itself. They took 56 ions in a trap and wove them into a three-dimensional cloud of entangled particles.

A phase transition is like the moment water turns into ice. In the quantum world, such transitions occur at absolute zero, and seeing them directly is nearly impossible. Usually, this requires building extremely complex computer models that demand enormous resources. The Delta-VQE method offers a workaround.

A black hole's horizon is not a wall but rather a one-way membrane. Anything that crosses it disappears forever. Stephen Hawking showed that this boundary should glow faintly, emitting particles. But catching such radiation from a real black hole is impossible: it's too far and too dim. Physicists have found a workaround: build a "toy" black hole out of magnetic atoms.

Electrons in a solid usually either run freely (metal) or are locked in place (insulator). But sometimes strong mutual repulsion locks them into a halfway state: charges stand still, while spins, tiny magnetic arrows, continue to live their own life. This is called a Mott insulator.

Water boils at one hundred degrees — everyone knows that. But why exactly one hundred? Why not smoothly, but abruptly: a second ago it was liquid, and suddenly — bubbles, steam, bubbling. Such sharp changes are called phase transitions, and they have a rigorous mathematical foundation.

Machine learning has long ceased to be just a tool — it is becoming an investigator, independently fishing out the laws of nature from data. But how does a silicon mind come to understand?

Some materials are internally like a Möbius strip: their electronic states are twisted in a special way. Such topological properties are usually manipulated with a powerful magnetic field, as if trying to flatten the strip with a sledgehammer. A group of researchers has found a more delicate tool.

A long chain of atoms, each a tiny magnet. They talk to each other and to a common field, like musicians in an orchestra who hear both the conductor and their neighbors. When the external field changes, the orchestra either plays out of sync or all instruments come in together: that's a quantum phase transition.

If you squeeze an ordinary piece of metal, it heats up — even those who have pumped a bicycle tire know that. But what happens if you squeeze a magnet in which atomic arrows refuse to freeze even at absolute zero?

If you check where an electron is every second, its quantum properties change. It's like a child playing hide-and-seek but constantly being called by name: they freeze and stop running. In the particle world, such a "caller" is a measurement. It prevents particles from freely forming a shared quantum state, or entanglement.

Tiny magnets on a lattice, the classic Ising model, are usually described by how neighbors influence each other. But what happens when the system is closely watched? Each measurement of a coupling energy is like a gaze that forces the magnets to 'decide' their state.

Magnetic materials can sometimes behave like a group of people who just can't agree: some bonds between atoms pull one way, others the opposite. When such conflicts pile up, the system becomes 'frustrated'—it can't settle into a single state of rest.

The crystal changes its internal geometry like a building frame that slightly twists during an earthquake. In the manganese-gallium alloy (Mn₃Ga), at around 485 Kelvin (about 212°C), a magnetic transition occurs: the atoms align into an antiferromagnetic order, where neighboring magnetic…

A diary loses pages, yet the story migrates to the rest. Black holes act similarly: as they shrink (shown by Stephen Hawking), swallowed information shouldn't vanish; it eventually resurfaces. Theory predicts a specific rise-and-fall curve for this escape.

Electrons in a conductor behave like a crowd on an escalator: each one moves on its own, but together they create a flow. If you make them circle around a ring, their angular momentum (a measure of rotation) can couple to a magnetic field, like gears in a clock.

A magnetic film divided into tiny arrow-shaped cells behaves like a crowd in a square. While it's cold, all arrows point in the same direction — perfect order. Heat the film, and the arrows start darting around like pedestrians who have lost their purpose. Somewhere between these extremes, there is a moment when the system stops being uniform but hasn't yet dissolved into random noise.

A crowd of people in a subway station moves slower than individuals: everyone gets in everyone else's way. A similar picture emerges in a dense cloud of magnetic atoms exchanging energy. Previously, it was thought that the transfer rate depended only on the atoms' own properties.

Physicists built a chain of Rydberg atoms — atoms with electrons in enormous orbits, comparable to planetary paths. These giant atoms feel their neighbors intensely, turning the chain into a quantum analog of a string.

A pendulum receives a kick but returns to its starting position not after one period, but after two. That is how a discrete time crystal behaves: a phase of matter that spontaneously breaks discrete time-translation symmetry and oscillates with a period that is a multiple of the driving period.

Two actors on the same stage. One is a fermion, finicky and demanding, hard to make follow the rules of a quantum simulator. The other is a boson, easygoing and undemanding, ready to take any role. The director hopes the audience won't notice the substitution.

A crowd in a square. At first, everyone spins to their own rhythm, but suddenly the music changes, and they all start moving in sync, as one. That's roughly how electrons behave in some metals: they either cling to magnetic impurities or break away and form a collective order.