In physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, a toy model is a simplified set of objects and equations relating them that can nevertheless be used to understand a mechanism that is also useful in the full, non-simplified theory.

• In "toy" mathematical models, this is usually done by reducing the number of dimensions or reducing the number of fields/variables or restricting them to a particular symmetric form.
• In "toy" physical descriptions, an everyday example of an analogous mechanism is often used to illustrate an effect in order to make the phenomenon easier to visualize.

Some examples of "toy models" in physics might be: the Ising model

Ising model

The Ising model is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables called spins that can be in one of two states . The spins are arranged in a graph , and each spin interacts with its nearest neighbors...

 as a toy model for ferromagnetism

Ferromagnetism

Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished...

, or, more generally, as one of the simplest examples of lattice models

Lattice model (physics)

In physics, a lattice model is a physical model that is defined on a lattice, as opposed to the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. Currently, lattice models are...

; orbital mechanics described by assuming that the Earth is attached to the Sun by a large elastic band; Hawking radiation

Hawking radiation

Hawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...

 around a black hole

Black hole

A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

 described as conventional radiation from a fictitious membrane at radius r=2M (the black hole membrane paradigm

Membrane paradigm

In black hole theory, the black hole membrane paradigm is a useful "toy model" method or "engineering approach" for visualising and calculating the effects predicted by quantum mechanics for the exterior physics of black holes, without using quantum-mechanical principles or calculations...

); frame-dragging

Frame-dragging

Einstein's general theory of relativity predicts that non-static, stationary mass-energy distributions affect spacetime in a peculiar way giving rise to a phenomenon usually known as frame-dragging...

 around a rotating star considered as the effect of space being a conventional "draggable" fluid.

The phrase "Tinker-toy model" is also sometimes used in this context, and refers to a particular children's construction toy that allows objects to be built easily but somewhat unrealistically.

See also

• Toy theorem
  Toy theorem
  In mathematics, a toy theorem is a simplified version of a more general theorem. For instance, by introducing some simplifying assumptions in a theorem, one obtains a toy theorem....
  
  
• Toy problem
  Toy problem
  In scientific disciplines, a toy problem is a problem that is not of immediate scientific interest, yet is used as an expository device to illustrate a trait that may be shared by other, more complicated, instances of the problem, or as a way to explain a particular, more general, problem solving...
  
  
• Scientific modeling
• Spekkens Toy Model
  Spekkens Toy Model
  The Spekkens toy model is a conceptually simple model, introduced by Robert Spekkens in 2004, to argue in favour of the epistemic view of quantum mechanics...