Phase diagrams of U(1) lattice Higgs models

Phase diagrams for charge-one and charge-two scalar particles in compact QED are constructed using Monte Carlo methods on the ICL DAP computer. The results are in agreement with the features predicted by Fradkin and Shenker and with known and new limiting cases.     

Phase structure of a U(1) lattice gauge theory with dual gauge fields

We introduce a U(1) lattice gauge theory with dual gauge fields and study its phase structure. This system is partly motivated by unconventional superconductors like extended s-wave and d  -wave superconductors in the strongly-correlated electron systems and also studies of the t–J$t\text{–}J$ model in the slave-particle representation. In this theory, the “Cooper-pair” (or RVB spinon-pair) field is put on links of a cubic lattice due to strong on-site repulsion between original electrons in contrast to the ordinary s  -wave pair field on sites. This pair field behaves as a gauge field dual to the U(1) gauge field coupled with the hopping of electrons or quasi-particles of the t–J$t\text{–}J$ model, holons and spinons. By Monte Carlo simulations we study this lattice gauge model and find a first-order phase transition from the normal state to the Higgs (superconducting) phase. Each gauge field works as a Higgs field for the other gauge field. This mechanism requires no scalar fields in contrast to the ordinary Higgs mechanism. An explicit microscopic model is introduced, the low-energy effective theory of which is viewed as a special case of the present model.     

Large-N lattice models with mixed actions

U(N) lattice gauge theories and spin systems with mixed fundamental and adjoint representation actions are studied. Exact results are found for two-dimensional gauge theories and one-dimensional spin chains. Phase diagrams for higher-dimensional systems are found using mean field theory. Various implications of this work are discussed.     

Neutral current phenomenology of supersymmetric SU(2) × U(1) × ≈U(1) models

The neutral current sector of a class of supersymmetric SU(2) × U(1) × ≈U(1) models is parametrized. Bounds on the neutral boson masses are obtained from the low energy data, and the implications of future experimental findings for these models are discussed.     

Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with N-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N = 1 model. For N = 2, we found that the system has a second-order phase transition line in the c₂ (gauge coupling)-c₁ (Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N = 3, we found that there exists a critical line similar to that in the N = 2 model, but the critical line is separated into two parts; one for c₂<c_2tc=2.4±0.1 with first-order transitions, and the other for c_2tc<c₂ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N = 4 and N = 5 systems. We also studied the case of anistropic Higgs coupling in the N = 3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an “enhancement” of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.     

Distinguishability ofSU(2)×U(1)×U′(1) andSO(10) gauge models from the Weinberg-Salam model

The predictions ofSU(2)×U(1)×U′(1) andSO(10) gauge models for the asymmetry parametersA-,B-,C _L andC _R in the deep inelastic scattering of polarized electrons and positrons by unpolarized protons and deuterons are compared with those calculated in the Weinberg Salam model for different values ofy. The model based on,SU(2)×U(1)×U′(1) group has been found almost indistinguishable from the Weinberg Salam model with regard to the parametersA-,B- andC _L (except forB- in the region 0≦y≦0.2) althoughC _R exhibits marked distinguishability. TheSO(10) model, for certain choice of its model parameters, can be distinguished from the Weinberg Salam model through measurement of the asymmetry parameters for different values ofy.     

Phase structure of a 3D nonlocal U(1) gauge theory: deconfinement by gapless matter fields

In this paper, we study a 3D compact U(1) lattice gauge theory with a variety of nonlocal interactions that simulates the effects of gapless/gapful matter fields. We restrict the nonlocal interactions among gauge variables only to those along the temporal direction and adjust their coupling constants optimally to simulate the isotropic nonlocal couplings of the original model. This theory is quite important to investigate the phase structures of QED₃ and strongly-correlated electron systems like the 2D quantum spin models, the fractional quantum Hall effect, the $t\text{–}J$ model of high-temperature superconductivity. We perform numerical studies of this theory to find that, for a certain class of power-decaying couplings, there appears a second-order phase transition to the deconfinement phase as the gauge coupling constant is decreased. On the other hand, for the exponentially-decaying coupling, there are no signals for second-order phase transition. These results indicate the possibility that introduction of sufficient number of massless matter fields destabilizes the permanent confinement in the 3D compact U(1) pure gauge theory due to instantons.     

Neutral current constraints in the SU(2) ⊗ U(1) models

We present a systematic analysis of hadronic neutral currents in low energy neutrino reactions applicable to SU(2) ? U(1) models with any number of quarks. We point out a relation to determine the Weinberg angle independent of the models for the heavy quarks. We discuss the constraints of atomic neutral current experiments on the SU(2) ? U(1) gauge models.     

Exact consequences of universality in SU(2) × U(1) gauge models

Exact consequences of universality within SU(2) × U(1) gauge models, with leptons in doublets and singlets, and for arbitrary vacuum expectation values of the Higgs fields, imply an extended Weinberg-Salam structure for leptons, with all neutrinos massless (the inverse statement is obvious). We also discuss approximate universality.     

Phase structure of generalized Gross-Neveu models

A phase structure of models (1) withn spinor multiplets has been considered in the space-time of dimensionD=2,3. In the case whenn=2 andD=3 there may occur vacuums |+> violating chiral invariance, as well as |?> violatingP,T symmetry of the model. Atn, D=2 there may exist a phase, where a hierarchy of fermion multiplet masses arises in a dynamical way. The properties of Gross-Neveu model have been dealt with atD=3,n=1 and the temperature and chemical potential not equal to zero.     

Phase structure of U(N→∞) gauge theory on a two-dimensional lattice for a broad class of variant actions

It is pointed out that finding the partition function for U(N) gauge theory on a two-dimensional lattice in the limit N→∞ reduces, for a broad class of single-plaquette actions, to a well-known and solved mathematical problem. The case where in the single plaquette action the matrix U + U⁺ occuring in Wilson's formula is replaced by an arbitrary polynomial in this matrix, is discussed in detail and explicit results for the second-order polynomial are presented. A rich phase structure with second- and third-order phase transitions is found. The results are shown to have at the qualitative level a simple thermodynamical interpretation. They support the view that the phase structure of a lattice gauge theory is an artifact of the lattice action used rather than some reflection of the underlying group structure.     

A minimalSU(2)×U(1)×U(1) electroweak model with mirror fermions

We present a minimal extension of the standard electroweak model, which accommodates mirror fermions, based onSU(2)×U(1)×U(1). Mirror mixing happens through sterile neutrino states and induces radiative mixing for charged leptons. Quarks and mirror quarks are not mixed with each other, consistent with the suppression of flavour changing neutral currents. Higgs sector, fermion masses and neutral currents are discussed. In this scheme there can be a secondZ boson as light as 0.2TeV.     

Massless and supermassive quarks in some SU(3) × U(1) models

We consider an SU(3) × U(1) model with natural symmetry. We exhibit difficulties with the model for the simplest Higgs structure, but by extending it obtain the Cabibbo angle if one quark is very heavy. Difficulties with naturality persist for leptons.