In physics, 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 phenomen easier to visualise.
Some examples of "toy models" in physics might be: the Ising model as a toy model for ferromagnetism, or, more generally, as one of the simplest examples of lattice models; orbital mechanics described by assuming that the Earth is attached to the Sun by a large elastic band; Hawking radiation around a black hole described as conventional radiation from a fictitious membrane at radius r=2M (the black hole membrane paradigm); frame-dragging around a rotating star considered as the effect 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.
