In physics, spontaneous symmetry breaking occurs when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. When that happens, the system no longer appears to behave in a symmetric manner. It is a phenomenon that naturally occurs in many situations.
The symmetry group can be discrete, such as the space group of a crystal, or continuous (e.g., a Lie group), such as the rotational symmetry of space. However if the system contains only a single spatial dimension then only discrete symmetries may be broken in a vacuum state of the full quantum theory, although a classical solution may break a continuous symmetry.
A common example to help explain this phenomenon is a ball sitting on top of a hill. This ball is in a completely symmetric state. However, its state is unstable: the slightest perturbing force will cause the ball to roll down the hill in some particular direction. At that point, symmetry has been broken because the direction in which the ball rolled has a feature that distinguishes it from all other directions.
Contents 
In the simplest example, the spontaneously broken field is described by a scalar field theory. In physics, one way of seeing spontaneous symmetry breaking is through the use of Lagrangians. Lagrangians, which essentially dictate how a system will behave, can be split up into kinetic and potential terms
It is in this potential term (V(φ)) that the action of symmetry breaking occurs. An example of a potential is illustrated in the graph at the right.
This potential has many possible minima (vacuum states) given by
for any real θ between 0 and 2π. The system also has an unstable vacuum state corresponding to Φ = 0. This state has a U(1) symmetry. However, once the system falls into a specific stable vacuum state (corresponding to a choice of θ) this symmetry will be lost or spontaneously broken.
In the Standard Model, spontaneous symmetry breaking is accomplished by using the Higgs boson and is responsible for the masses of the W and Z bosons. A slightly more technical presentation of this mechanism is given in the article on the Yukawa interaction, where it is shown how spontaneous symmetry breaking can be used to give mass to fermions.
More generally, we can have spontaneous symmetry breaking in nonvacuum situations and for systems not described by actions. The crucial concept here is the order parameter. If there is a field (often a background field) which acquires an expectation value (not necessarily a vacuum expectation value) which is not invariant under the symmetry in question, we say that the system is in the ordered phase and the symmetry is spontaneously broken. This is because other subsystems interact with the order parameter which forms a "frame of reference" to be measured against, so to speak.
If a vacuum state obeys the initial symmetry then the system is said to be in the Wigner mode, otherwise it is in the Goldstone mode.
On October 7, 2008, the Royal Swedish Academy of Sciences awarded the 2008 Nobel Prize in Physics to two Japanese citizens and a Japaneseborn American for their work in subatomic physics. American Yoichiro Nambu, 87, of the University of Chicago, won half of the prize for the discovery of the mechanism of spontaneous broken symmetry. Japanese physicists Makoto Kobayashi and Toshihide Maskawa shared the other half of the prize for discovering the origin of the broken symmetry.^{[1]} The trio shared the 10 million kronor (1.25 million USD) purse, as well as a diploma and an invitation to the prize ceremonies in Stockholm on December 10, 2008.
Spontaneous Symmetry Breaking is a way that scientists start off with something completely symmetrical and end up (without creating an outside force) with something nonsymmetrical. Spontaneous means sudden or unexpected. Symmetry (Latin sym meaning united, metric meaning measure) refers to the fact that rules (known as symmetries) of physics that are changed. Breaking refers to the change of the symmetry. Spontaneous Symmetry Breaking commonly happens in the theoretical Higgs effect.
Spontaneous Symmetry Breaking can create a theoretical particle called a Higgs Boson. This is a particle which is predicted to be able to give mass to certain particles called bosons, like a photon. Also, many scientists believe in the Higgs Effect (which is very similar to Spontaneous Symmetry Breaking) to answer questions that are not answered in the Standard model of physics. The Standard model predicts that certain types of quarks should have a mass of zero, while in reality they have a nonzero mass value. Some scientists believe that Spontaneous Symmetry Breaking is the answer.
For Spontaneous Symmetry Breaking to happen, you need an environment which is completely symmetrical, and has at least two outcomes that are equally likely. Spontaneous Symmetry Breaking starts with two particles that are completely equal; their spin is equal, too. Mathematically, Spontaneous Symmetry Breaking can be extremely puzzling, since you start out with two identical things and end up with two nonidentical things. However, in practice, it is not so puzzling. If you have two particles moving at each other with equal speed, it would seem impossible for either of them to do anything but be symmetrical. However, if each particle has an equal 5050 chance to be spinning one way or another, it is possible–in theory and in practice–to have this symmetry broken. It begins with symmetry to start with because the particles have an equal and symmetrical 5050 chance of spinning one way or another.
Scientists have been able to use Spontaneous Symmetry Breaking. However, it has not proven (or disproven) the theory of the Higgs Boson. The energy required to generate a Higgs Boson is simply too powerful for the particle accelerators that we have available. However, the future will probably reveal the existence or nonexistence of the Higgs Boson.
Particles in Physics  

Elementary:  Fermions:  Quarks: up  down  strange  charm  bottom  top Leptons: electron  muon  tau  neutrinos  
Bosons:  Gauge bosons: photon  W and Z bosons  gluons  
Composite:  Hadrons:  Baryons: proton  neutron  hyperon  
Mesons: pion  kaon  J/ψ  
Atomic nuclei  Atoms  Molecules  
Hypothetical:  Higgs boson  Graviton  Tachyon 
