Editing Toy model

{{Short description|Deliberately simplistic scientific model}}
{{For|actual toys|model figure|action figure}}
{{More references|date=December 2009}}
{{Wikt}}
In [[scientific modeling]], 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''',{{clarify|is this in mathematics in general, or mathematical physics?|date=December 2016}} 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 '''[[Economic model|economic models]]''', some may be only loosely based on theory, others more explicitly so. 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's list of examples includes the [[IS–LM model]], the [[Mundell–Fleming model]], the [[RBC model]], and the [[New Keynesian model]].<ref>3.	Blanchard O., 2018- '''On the future of macroeconomic models''', ''[[Oxford Review of Economic Policy]]'', Volume 34, Numbers 1–2, 2018, p.p.52-53.</ref> 
* In '''"toy" physical descriptions''', an analogous example of an everyday mechanism is often used for illustration.

The phrase '''"tinker-toy model"''' is also used,{{fact|date=December 2016}} in reference to the [[Tinkertoy]]s product used for children's [[constructivist learning]].

==Examples==
Examples of toy models in physics include:

* the [[Ising model]] as a toy model for [[ferromagnetism]], or [[lattice model (physics)|lattice models]] more generally. It is the simplest model that allows for [[Euclidean field theory|Euclidean]] [[quantum field theory]] in [[statistical physics]].<ref>{{Cite book|last1=Hartmann|first1=Alexander K.|url=https://books.google.com/books?id=6zdd5N8DCmEC&q=%22toy+model%22++ferromagnetism&pg=PA104|title=Phase Transitions in Combinatorial Optimization Problems: Basics, Algorithms and Statistical Mechanics|last2=Weigt|first2=Martin|date=2006-05-12|publisher=John Wiley & Sons|isbn=978-3-527-60686-3|pages=104|language=en}}</ref><ref>{{Cite web|title=Ising model|url=http://nlab-pages.s3.us-east-2.amazonaws.com/nlab/show/Ising+model|access-date=2022-01-12|website=nlab-pages.s3.us-east-2.amazonaws.com|language=en}}</ref><ref>{{Cite web|title=The Ising Model|url=https://stanford.edu/~jeffjar/statmech/intro4.html|access-date=2022-01-12|website=stanford.edu}}</ref>
* Newtonian [[orbital mechanics]] as described by assuming that Earth is attached to the Sun by an elastic band;
* the [[Schwarzschild metric]], general relativistic model describing a single symmetrical non-rotating non-charged concentration of mass (such as a perfect spherical mass): a simple relativistic "equivalent" of the classical symmetric Newtonian mass (in fact, the first [[solution of the Einstein field equations]] to be developed);
* [[Hawking radiation]] around a [[black hole]] described as conventional radiation from a fictitious membrane at radius [[r=2M|{{math|1= 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 [[null dust]];
* the [[Gödel metric]] in general relativity, which allows [[closed timelike curves]];
* the [[Lambda-CDM model]] of cosmology, in which general relativistic effects of structure formation are not taken into account.<ref>{{Cite journal|last1=Buchert|first1=T.|last2=Carfora|first2=M.|last3=Ellis|first3=G. F. R.|last4=Kolb|first4=E. W.|last5=MacCallum|first5=M. A. H.|last6=Ostrowski|first6=J. J.|last7=Räsänen|first7=S.|last8=Roukema|first8=B. F.|last9=Andersson|first9=L.|last10=Coley|first10=A. A.|last11=Wiltshire|first11=D. L.|date=2015-11-05|title=Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?|journal=Classical and Quantum Gravity|volume=32|issue=21|pages=215021|doi=10.1088/0264-9381/32/21/215021|arxiv=1505.07800|bibcode=2015CQGra..32u5021B|issn=0264-9381|hdl=10138/310154|s2cid=51693570|hdl-access=free}}</ref>
* the [[empty universe]], a simple expanding universe model;
* the [[Bohr model]] of the atom, a "semi-classical" quantum mechanical model of the atom, which can be solved exactly for the hydrogen atom;
* the [[particle in a box]] in quantum mechanics;
* the [[Spekkens toy model|Spekkens model]], a [[hidden-variable theory]];
* the [[primon gas]], which illustrates some connections between [[number theory]] and physics.

==See also==
* {{annotated link|Physical model}}
* {{annotated link|Spherical cow}}
* {{annotated link|Toy problem}}
* {{annotated link|Toy theorem}}

==References==
{{Reflist}}

[[Category:Metaphors]]
[[Category:Mathematical terminology]]
[[Category:Economics models]]
[[Category:Theoretical physics]]