In the
modeling of
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
, a toy model is a deliberately simplistic model with many details removed so that it can be used to explain a mechanism concisely. It is also useful in a description of the fuller model.
* In "toy" mathematical models, this is usually done by reducing or extending the number of dimensions or reducing the number of fields/variables or restricting them to a particular symmetric form.
* In Macroeconomics modelling, are a class of models, some may be only loosely based on theory, others more explicitly so. But they have the same purpose. They allow for a quick first pass at some question, and present the essence of the answer from a more complicated model or from a class of models. For the researcher, they may come before writing a more elaborate model, or after, once the elaborate model has been worked out. Blanchard list of examples includes IS–LM model, the
Mundell–Fleming model, the RBC model, and the New Keynesian model.
* In "toy" physical descriptions, an analogous example of an everyday mechanism is often used for illustration.
The phrase "tinker-toy model" is also used, in reference to the popular
Tinkertoys used for children's
constructivist learning.
Examples
Examples of toy models in physics include:
* the
Ising model
The Ising model () (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent ...
as a toy model for
ferromagnetism
Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
, or
lattice models more generally. It is the simplest model that allows for
Euclidean Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
in
statistical physics
Statistical physics is a branch of physics that evolved from a foundation of statistical mechanics, which uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approxim ...
*
orbital mechanics as described by assuming that Earth is attached to the Sun by an elastic band;
*
Hawking radiation around a
black hole
A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can def ...
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 of space being a conventional viscous fluid.
*the
concordance model of cosmology, in which general relativistic effects of structure formation are not taken into account.
Spekkens model
See also
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*
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References
{{DEFAULTSORT:Toy Model
Mathematical terminology
Theoretical physics