Computation of the vortex free energy in SU(2) gauge theory

We present the first measurement of the vortex free-energy order parameter at weak coupling for SU(2) in simulations employing multihistogram methods. The result shows that the excitation probability for a sufficiently thick vortex in the vacuum tends to unity. This is rigorously known to provide a necessary and sufficient condition for maintaining confinement at weak coupling in SU(N) gauge theories.     

Coupled gap equations for the screening masses in the SU(2) Higgs model

The complete set of static screening masses is determined for the SU(2) Higgs model from one-loop coupled gap equations. Results from the version containing scalar fields both in the fundamental and adjoint representations are compared with the model arising when integration over the adjoint scalar field is performed. A non-perturbative and non-linear mapping between the couplings of the two models is proposed which exhibits perfect decoupling of the heavy adjoint scalar field. Also the alternative of a gauge invariant mass resummation is investigated in the high temperature phase. Received: 7 May 1999 / Revised version: 6 July 1999 / Published online: 16 November 1999     

The renormalization flow in the adjoint SU(2) lattice Higgs model

Applying the Monte Carlo renormalization group method we investigate the flow of coupling constants for the 8⁴ and 16⁴ SU(2) lattice Higgs model with triplet Higgs fields. The couplings of the renormalized actions are determined using Schwinger-Dyson equations. From the flow we find new evidence for the existence of a tricritical point at finite values of the inverse gauge coupling β but no indication for a discontinuity fixed point.     

The U(1) Higgs model

By using rigorous renormalization group methods we construct the continuum limit of the finite-volume lattice U(1) Higgs model in two and three dimensions. The method relies on a proof of the convergence of the effective action.Research supported in part by the National Science Foundation under grants PHY 82-03669 and PHY 81-17463     

On condensation of the vortex solitons in a 2 + 1 dimensional abelian Higgs model

We study the roles of the vortex solitons in a 2 + 1 dimensional abelian Higgs model. From the effective lagrangian L_eff for the soliton field χ, it is found that the appearance of the solitons reduces the dielectric constant to a value smaller than one. If the Higgs field 〈H〉_vac does not vanish, the vacuum is in the Higgs phase and the solitons are not important. If it does vanish, the solitons become massless and L_eff has an infinite number of classically degenerate vacua. In the quantum theory of L_eff with large coupling constant e, no evidence of 〈χ〉_vac ≠ 0 has been discovered. For this conclusion to hold it is crucial that the free energy of scalar QED monotonically increases with e².     

The Phase Transition Generated by Radial Mode of the Higgs Field in Lattice Z(2) Gauge-Higgs Model

We study the 4-dimensional lattice Z(2) gauge-Higgs theory in the variational cumulant expansion approach. It is shown that the existence of the first drder phase transition between Higgs and confinement regions is fundamentally dependent on the fluctuation of the radial mode of the scalar (Higgs) field.     

The phase transition generated by the radial mode of the scalar field in the lattice Z(2) gauge-Higgs model

For the lattice Z(2) gauge-Higgs model with a radially variable scalar field, it is rigorously shown that the first-order phase transition is generated by the radial mode of the scalar field, at least, in the strong gauge-coupling limit β = 0. This phenomena was first observed by Munehisa and Munehisa, using Monte Carlo method and explained by mean field (approximation) method. We prove the statement for a simple case in which the Higgs scalar field takes only 3 values.     

TheU(1) Higgs model

We construct the infinite volume limit of theU(1) Higgs model in two and three dimensions, and verify some of the Osterwalder-Schrader axioms. The proof uses a combination of renormalization group techniques and correlation inequalities.     

Strong self-coupling expansion in the lattice-regularized standard SU(2) Higgs model

Expectation values at an arbitrary point of the 3-dimensional coupling parameter space in the lattice-regularized SU(2) Higgs model with a doublet scalar field are expressed by a series of expectation values at infinite self-coupling (λ = ∞). Questions of convergence of this “strong self-coupling expansion” (SSCE) are investigated. The SSCE is a potentially useful tool for the study of the γ-dependence at any value (zero or non-zero) of the bare gauge coupling.     

The free energy of the spin-boson model

Forn spins 1/2 coupled linearly to a boson field in a volumeV _n, the existence of the specific free energy is proved in the limitn ,V _n withn/V _n=const. The interaction is essentially of the mean field type, in as much as it is proportional to 1/V _n; the coupling constants are allowed to be spin dependent. A variational expression is obtained for the limiting specific free energy, and a critical temperature is identified above which the system behaves as if there were no coupling at all.     

Mean field theory and the SU(2) adjoint Higgs model

Three versions of the mean field approximation are applied to determine the phase diagram of the SU(2) adjoint Higgs model. In two of these, one with gauge fixing and one without, the Higgs action is integrated exactly. In the third version, the Higgs and Wilson parts of the action are treated on equal footing. The results, when compared to those from Monte Carlo simulations, suggest that more accurate simulations are needed in the crossover region.