The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions.
The Lagrangian for the model is where the scalar field is complex,
is the electromagnetic field tensor, and
the covariant derivative containing the electric charge
there is a spontaneous breaking of the gauge symmetry at low energies, a variant of the Higgs mechanism.
On the other hand, if the squared mass is positive,
However, as was shown by Sidney Coleman and Erick Weinberg, even if the renormalized mass is zero, spontaneous symmetry breaking still happens due to the radiative corrections (this introduces a mass scale into a classically conformal theory - the model has a conformal anomaly).
In the broken phase the fluctuations of the scalar field
will manifest themselves as a naturally light Higgs boson, as a matter of fact even too light to explain the electroweak symmetry breaking in the minimal model - much lighter than vector bosons.
There are non-minimal models that give a more realistic scenarios.
Also the variations of this mechanism were proposed for the hypothetical spontaneously broken symmetries including supersymmetry.
Equivalently one may say that the model possesses a first-order phase transition as a function of
The model is the four-dimensional analog of the three-dimensional Ginzburg–Landau theory used to explain the properties of superconductors near the phase transition.
The three-dimensional version of the Coleman–Weinberg model governs the superconducting phase transition which can be both first- and second-order, depending on the ratio of the Ginzburg–Landau parameter
Historically, the order of the superconducting phase transition was debated for a long time since the temperature interval where fluctuations are large (Ginzburg interval) is extremely small.
that distinguishes type-I and type-II superconductors (see also here) is large enough, vortex fluctuations becomes important which drive the transition to second order.
The tricritical point lies at roughly
The prediction was confirmed in 2002 by Monte Carlo computer simulations.
[2] This quantum mechanics-related article is a stub.