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 e of the electromagnetic field. Assume that \lambda is nonnegative. Then if the mass term is tachyonic, m^2<0 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, m^2>0 the vacuum expectation of the field \phi is zero. At the classical level the latter is true also if m^2=0. 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). The same can happen in other gauge theories. In the broken phase the fluctuations of the scalar field \phi 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 m^2. 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, with a tricritical point near which separates type I from type II superconductivity. 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. The question was finally settled in 1982. If the Ginzburg–Landau parameter \kappa 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 , i.e., slightly below the value where type-I goes over into type-II superconductor. The prediction was confirmed in 2002 by Monte Carlo computer simulations.

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