In the
modeling
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure.
Models c ...
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 r ...
, 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 Mundell–Fleming model, also known as the IS-LM-BoP model (or IS-LM-BP model), is an economic model first set forth (independently) by Robert Mundell and Marcus Fleming. Reprinted in Reprinted in The model is an extension of the IS–LM ...
, 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
Tinkertoy
The Tinkertoy Construction Set is a toy construction set for children. It was designed in 1914—six years after the Frank Hornby's Meccano sets—by Charles H. Pajeau, who formed the Toy Tinker Company in Evanston, Illinois to manufactu ...
s used for children's
constructivist learning
Constructivism may refer to:
Art and architecture
* Constructivism (art), an early 20th-century artistic movement that extols art as a practice for social purposes
* Constructivist architecture, an architectural movement in Russia in the 1920s a ...
.
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
In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of co ...
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 Mathematics, mathematical tools for dealing with large populations ...
*
orbital mechanics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of ...
as described by assuming that Earth is attached to the Sun by an elastic band;
*
Hawking radiation
Hawking radiation is theoretical black body radiation that is theorized to be released outside a black hole's event horizon because of relativistic quantum effects. It is named after the physicist Stephen Hawking, who developed a theoretical a ...
around a
black hole
A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
described as conventional radiation from a fictitious membrane at radius
r=2M
The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an
exact solution to ...
(the black hole
membrane paradigm
In black hole theory, the black hole membrane paradigm is a simplified model, useful for visualising and calculating the effects predicted by quantum mechanics for the exterior physics of black holes, without using quantum-mechanical principles or ...
);
*
frame-dragging
Frame-dragging is an effect on spacetime, predicted by Albert Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary field is one that is in a steady state, but the masses ca ...
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
*
*
*
*
References
{{DEFAULTSORT:Toy Model
Mathematical terminology
Theoretical physics