Kertész line in the three-dimensional compact U(1) lattice Higgs model

The three-dimensional lattice Higgs model with compact U(1) gauge symmetry and unit charge is investigated by means of Monte Carlo simulations. The full model with fluctuating Higgs amplitude is simulated, and both energy as well as topological observables are measured. The data show a Higgs and a confined phase separated by a well-defined phase boundary, which is argued to be caused by proliferating vortices. For fixed gauge coupling, the phase boundary consists of a line of first-order phase transitions at small Higgs self-coupling, ending at a critical point. The phase boundary then continues as a Kertész line across which thermodynamic quantities are non-singular. Symmetry arguments are given to support these findings.     

A disorder parameter that test for confinement in gauge theories with quark fields

We propose to use a suitably defined vortex free energy as a disorder parameter in gauge field theories with matter fields. It is supposed to distinguish between the confinement phase, massless phase(s) and Higgs phase where they exist. The matter fields may transform according to an arbitrary representation of the gauge group. We compute the vortex free energy by series expansion for a Z₂ Higgs model and for SU(2) lattice models with quark or Higgs fields in the fundamental representation at strong coupling (confinement phase), and for the Z₂ Higgs model in the range of validity of low-temperature expansions (Higgs phase). The results are in agreement with the expected behavior.     

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.     

Topology of quantum gauge fields and duality (I): Yang-Mills-Higgs system in 2 + 1 dimensions

The basic role of the representation of the gauge group in characterizing the topological excitations of the vacuum is pointed out. For SU(N) gauge fields on a lattice, the topological excitations are monopoles in the adjoint representation of the dual group ¹SU(N). This leads to a dual representation of the Yang-Mills-Higgs system in 2 + 1 dimensions. For SU(3) the deal theory in a scalar theory with discrete Weyl symmetry S₃. In the presence of adjoint Higgs fields the Weyl symmetry is broken in the Higgs phase but restored by pseudo-particles in the confinement phase.     

Quantum phase transition in lattice model of unconventional superconductors

In this paper we shall introduce a lattice model of unconventional superconductors (SC) like d-wave SC in order to study quantum phase transition at vanishing temperature (T). Finite-T counterpart of the present model was proposed previously with which SC phase transition at finite T was investigated. The present model is a noncompact U(1) lattice-gauge-Higgs model in which the Higgs boson, the Cooper-pair field, is put on lattice links in order to describe d-wave SC. We first derive the model from a microscopic Hamiltonian in the path-integral formalism and then study its phase structure by means of the Monte Carlo simulations. We calculate the specific heat, monopole densities and the magnetic penetration depth (the gauge-boson mass). We verified that the model exhibits a second-order phase transition from normal to SC phases. Behavior of the magnetic penetration depth is compared with that obtained in the previous analytical calculation using XY model in four dimensions. Besides the normal to SC phase transition, we also found that another second-order phase transition takes place within the SC phase in the present model. We discuss physical meaning of that phase transition.     

Monte Carlo studies with the ST-100 array processor

Monte Carlo simulations with the 100 Mflop ST-100 array processor are described. The architecture of the array processor and its applicability to large-scale numerical simulations is discussed. Results are presented for the Abelian Higgs model, a charge density wave transition in a quasi-one-dimensional system and the finite temperature phase transition inSU(3) lattice gauge theory.     

Infrared saturation and phases of gauge theories with BRST symmetry

We investigate the infrared limit of the quantum equation of motion of the gauge boson propagator in various gauges and models with a BRST symmetry. We find that the saturation of this equation at low momenta distinguishes between the Coulomb, Higgs and confining phase of the gauge theory. The Coulomb phase is characterized by a massless gauge boson. Physical states contribute to the saturation of the transverse equation of motion of the gauge boson at low momenta in the Higgs phase, while the saturation is entirely due to unphysical degrees of freedom in the confining phase. This corollary to the Kugo–Ojima confinement criterion in linear covariant gauges also is sufficient for confinement in general covariant gauges with BRST and anti-BRST symmetry, maximal Abelian gauges with an equivariant BRST symmetry, non-covariant Coulomb gauge and in the Gribov–Zwanziger theory.     

On Nambu monopole dynamics in a SU(2) lattice Higgs model

It is shown that an SU(2) Higgs model on a lattice is equivalent to the Georgi-Glashow model in the limit of a small coupling constant between the Higgs and gauge fields. It can therefore be concluded that the transition between the confinement and symmetric phases in a 3 + 1 dimensional SU(2) Higgs model at finite temperature is accompanied by condensation of Nambu monopoles. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 9, 577–580 (10 November 1997)     

Multi-layer structure in the strongly coupled 5D abelian Higgs model

We explore the phase diagram of the five-dimensional anisotropic Abelian Higgs model by Monte Carlo simulations. In particular, we study the transition between the confining phase and the four-dimensional layered Higgs phase. We find that, in a certain region of the lattice parameter space, this transition can be first order, and that each layer moves into the Higgs phase independently of the others (decoupling of layers). As the Higgs couplings vary, we find, using mean field techniques, that this transition may probably become second order. Received: 21 December 2001 / Published online: 12 April 2002     

The Weinberg-Salam model and early cosmology

The consequences for cosmology of the phase transition in which SU(2)×U(1) symmetry is broken in the Weinberg-Salam model are discussed. The qualitative arguments concerning the effect of the phase transition on the baryon-to-entropy ratio that were recently posed by Witten for the case of a Coleman-Weinberg light Higgs boson are confirmed through exact numerical computations, but some quantitative disagreement is found. The computations are extended to the case in which the light Higgs boson is not of the Coleman-Weinberg type and the nature of the phase transition is discussed. Other cosmological effects are considered.     

THE PHASE STRUCTURE OF 4-d U(1) HIGGS MODEL WITH RADIAL EXCITATION

On 4⁴ regular lattice, the phase structure of U(1) Higgs model-a U(1) lattice gauge theory coupled to a scalar (Higgs) field-has been studied by using modified Metropolis algorithm without freezing the radial excitation of the Higgs field carrying fundamental charge. The result shows that Higgs and confined regions are completelg separated by a first-order phase transition line and the phase diagram of our model.consists of three distinct phases. This feature greatly differs from that of the model with radially frozen Higgs field discussed by D.J.E.Callaway and L.J. Carson.^[1]     

Ground States of Quantum Antiferromagnets in Two Dimensions

We explore the ground states and quantum phase transitions of two-dimensional, spin S=1/2, antiferromagnets by generalizing lattice models and duality transforms introduced by Sachdev and Jalabert (1990, Mod. Phys. Lett. B4, 1043). The minimal model for square lattice antiferromagnets is a lattice discretization of the quantum nonlinear sigma model, along with Berry phases which impose quantization of spin. With full SU(2) spin rotation invariance, we find a magnetically ordered ground state with Néel order at weak coupling and a confining paramagnetic ground state with bond charge (e.g., spin Peierls) order at strong coupling. We study the mechanisms by which these two states are connected in intermediate coupling. We extend the minimal model to study different routes to fractionalization and deconfinement in the ground state, and also generalize it to cases with a uniaxial anisotropy (the spin symmetry groups is then U(1)). For the latter systems, fractionalization can appear by the pairing of vortices in the staggered spin order in the easy-plane; however, we argue that this route does not survive the restoration of SU(2) spin symmetry. For SU(2) invariant systems we study a separate route to fractionalization associated with the Higgs phase of a complex boson measuring noncollinear, spiral spin correlations: we present phase diagrams displaying competition between magnetic order, bond charge order, and fractionalization, and discuss the nature of the quantum transitions between the various states. A strong check on our methods is provided by their application to S=1/2 frustrated antiferromagnets in one dimension: here, our results are in complete accord with those obtained by bosonization and by the solution of integrable models.     

Phase structure of two-flavor QCD at finite chemical potential

We study the phase diagram of two-flavor QCD at imaginary chemical potentials in the chiral limit. To this end we compute order parameters for chiral symmetry breaking and quark confinement. The interrelation of quark confinement and chiral symmetry breaking is analyzed with a new order parameter for the confinement phase transition. We show that it is directly related to both the quark density as well as the Polyakov loop expectation value. Our analytical and numerical results suggest a close relation between the chiral and the confinement phase transition.     

Exothermic Transition to a Future Susy Universe

The Higgs sector of the MSSM may be extended to solve the μ problem by the addition of a gauge singlet scalar field. We consider an extended Higgs model. For simplicity we consider the case where all the fields in the scalar sector are real. We analyze the vacuum structure of the model. We address the question of an exothermic phase transition from a broken susy phase with electroweak symmetry breaking (our current universe) to an exact susy phase with electroweak symmetry breaking (future susy universe).     

Symmetry behavior in gauge theories

A theory of phase transition with symmetry restoration in gauge theories at high temperature is investigated. The phase transition may be of the first or of the second order depending on relations between coupling constants. It is noted that the possible existense of a limiting temperature cannot prevent the high-temperature symmetry restoration. In the theories without neutral currents, symmetry also can be affected by a magnetic field. However in most of the models with neutral currents symmetry restoration takes place not due to a magnetic field but due to massive vector fields, created simultaneously by the magnetic field sources. It is pointed out that in most of the theories with neutral currents an increase of external currents lead to symmetry restoration, while an increase of density results in a further increase of symmetry breaking. In some cases critical values of temperature and external fields and currents appear to be extremely small. At certain relations between coupling constants radiative corrections lead to the absence of symmetry breaking in gauge theories even at zero temperature and in the absence of any other external factors. Strong constraints on masses and coupling constants for the symmetry in the Higgs model to be broken are obtained. It is shown that energy of substance is nonconserved due to energy “pumping” from the non-observable Bose-condensate in the processes under consideration.     

The vortex free energy in the screening phase of the Z(2) Higgs model

The vortex free energy was proposed to distinguish between the confinement and the Higgs phase (in the sense of 't Hooft) in lattice gauge theory, when matter fields are present that transform according to an arbitrary representation of the gauge group. In this paper I consider the Z(2) Higgs model and calculate the vortex free energy in the screening part of the confining/screening phase of Fradkin and Shenker. The result does not agree with the expected behavior that corresponds to the structure of the phase diagram. Therefore the vortex free energy is no longer a good indicator for confinement when matter fields transform non-trivially under the center of the gauge group (such as Z(2) Higgs scalars).     

Disorder,local order and asymptotic freedom in spin and lattice gauge theories

We examine some aspects of the confinement problem from the point of view of simple molecular field and spin wave concepts applied to lattice gauge theory. Our main endeavour is to discover the reasons for the absence of a deconfining phase transition in 4 dimensions. The essential point we make is that the mechanism responsible for eliminating the transition is deeply related to, not to say implied by, asymptotic freedom, which is the principal characteristic of the system at low temperatures and short wavelenghts. Our analysis is built on the analogy of lattice gauge theories with 2-dimensional spin systems.     

Charge confinement and vacuum structure in the 1 + 1 dimensional Higgs model

We demonstrate that the 1 + 1 dimensional Higgs model is equivalent to the massive sine-Gordon model, and hence to the massive Schwinger model in a special case. We do this by deriving a dual Lagrangian which embodies instanton effects. Based on this equivalence, we discuss charge confinement and vacuum structure in the Lagrangian formalism.