Showing papers on "Explicit symmetry breaking published in 1999"

Collective Motion of Self-Propelled Particles: Kinetic Phase Transition in One Dimension

Abstract: We demonstrate that a system of self-propelled particles exhibits spontaneous symmetry breaking and self-organization in one dimension, in contrast with previous analytical predictions. To explain this surprising result we derive a new continuum theory that can account for the development of the symmetry broken state and belongs to the same universality class as the discrete self-propelled particle model.

Variants of fattening and flavor symmetry restoration

Abstract: We study the effects of different "fat link" actions for Kogut-Susskind quarks on flavor symmetry breaking. Our method is mostly empirical - we compute the pion spectrum with different valence quark actions on common sets of sample lattices. Different actions are compared, as best we can, at equivalent physical points. We find significant reductions in flavor symmetry breaking relative to the conventional or to the "link plus staple" actions, with a reasonable cost in computer time. We also develop and test a scheme for approximate unitarization of the fat links. While our tests have concentrated on the valence quark action, our results will be useful in designing simulations with dynamical quarks.

Application of p-adic analysis to models of breaking of replica symmetry

Abstract: Methods of p-adic analysis are applied to the investigation of spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for the Parisi replica matrix is given and, moreover, the Parisi replica matrix in models of spontaneous breaking of the replica symmetry in the simplest case is expressed in the form of the Vladimirov operator of p-adic fractional differentiation. Also, the model of hierarchical diffusion (that was proposed to describe relaxation of spin glasses) is investigated using p-adic analysis.

Phase transition and symmetry breaking in the minority game.

Abstract: We show that the minority game, a model of interacting heterogeneous agents, can be described as a spin system and displays a phase transition between a symmetric phase and a symmetry broken phase where the game's outcome is predictable. As a result a "spontaneous magnetization" arises in the spin formalism.

Quaternion symmetry in relativistic molecular calculations: The Dirac–Hartree–Fock method

Abstract: A symmetry scheme based on the irreducible corepresentations of the full symmetry group of a molecular system is presented for use in relativistic calculations. Consideration of time-reversal symmetry leads to a reformulation of the Dirac–Hartree–Fock equations in terms of quaternion algebra. Further symmetry reductions due to molecular point group symmetry are then manifested by a descent to complex or real algebra. Spatial symmetry will be restricted to D2h and subgroups, and it will be demonstrated that the Frobenius–Schur test can be used to characterize these groups as a whole. The resulting symmetry scheme automatically provides maximum point group and time-reversal symmetry reduction of the computational effort, also when the Fock matrix is constructed in a scalar basis, that is, from the same type of electron repulsion integrals over symmetry-adapted scalar basis functions as in nonrelativistic theory. An illustrative numerical example is given showing symmetry reductions comparable to the nonrela...

Patterns of Symmetry Breaking in QCD at High Baryon Density

Abstract: We study the structure of QCD at very large baryon density for an arbitrary number of flavors $N_f$. We provide evidence that for any number of flavors larger than $N_f=2$ chiral symmetry remains broken at asymptotically large chemical potential. For $N_c=N_f=3$, chiral symmetry breaking follows the standard pattern $SU(3)_L\times SU(3)_R\to SU(3)$, but for $N_f>3$ unusual patterns emerge. We study the case $N_f=3$ in more detail and calculate the magnitude of the chiral order parameters $ $ and $ $ in perturbative QCD. We show that, asymptotically, $ ^{1/3}$ is much smaller than $ ^{1/6}$. The result can be understood in terms of an approximate discrete symmetry.

Charge Order, Superconductivity, and a Global Phase Diagram of Doped Antiferromagnets

Abstract: We investigate the interplay between lattice symmetry breaking and superconducting order in a two-dimensional model of doped antiferromagnets, with long-range Coulomb interactions and $\mathrm{Sp}(2N)$ spin symmetry, in the large- $N$ limit. Our results motivate the outline of a global phase diagram for the cuprate superconductors. We describe the quantum transitions between the phases, the evolution of their fermion excitation spectrum, and the experimental implications.

From Asymmetry to Full Symmetry: New Techniques for Symmetry Reduction in Model Checking

Abstract: It is often the case that systems are "nearly symmetric"; they exhibit symmetry in a part of their description but are, nevertheless, globally asymmetric. We formalize several notions of near symmetry and show how to obtain the benefits of symmetry reduction when applied to asymmetric systems which are nearly symmetric. We show that for some nearly symmetric systems it is possible to perform symmetry reduction and obtain a bisimilar (up to permutation) symmetry reduced system. Using a more general notion of "sub-symmetry" we show how to generate a reduced structure that is simulated (up to permutation) by the original asymmetric program. In the symbolic model checking paradigm, representing the symmetry reduced quotient structure entails representing the BDD for the orbit relation. Unfortunately, for many important symmetry groups, including the full symmetry group, this BDD is provably always intractably large, of size exponential in the number of bits in the state space. In contrast, under the assumption of full symmetry, we show that it is possible to reduce a textual program description of a symmetric system to a textual program description of the symmetry reduced system. This obviates the need for building the BDD representation of the orbit relation on the program states under the symmetry group. We establish that the BDD representing the reduced program is provably small, essentially polynomial in the number of bits in the state space of the original program.

Heavy thresholds, slepton masses and the μ term in anomaly mediated supersymmetry breaking

Abstract: The effects of heavy mass thresholds on anomaly-mediated soft supersymmetry breaking terms are discussed. While heavy thresholds completely decouple to lowest order in the supersymmetry breaking, it is argued that they do affect the breaking terms at higher orders. The relevant contributions typically occur at lower order in the loop expansion compared to purely anomaly mediated contributions. The non decoupling contributions may be used to render models in which the only source of supersymmetry breaking is anomaly mediation viable, by generating positive contributions to the sleptons' masses squared. They can also be used to generate acceptable ?- and B-terms.

Enhanced global symmetries and the chiral phase transition

Abstract: We examine the possibility that the physical spectrum of a vectorlike gauge field theory exhibits an enhanced global symmetry near a chiral phase transition. A transition from the Goldstone phase to the symmetric phase is expected as the number of fermions ${N}_{f}$ is increased to some critical value. Various investigations have suggested that a parity-doubled spectrum develops as the critical value is approached. Using an effective Lagrangian as a guide, we note that parity doubling is associated with the appearance of an enhanced global symmetry in the spectrum of the theory. The enhanced symmetry would develop as the spectrum splits into two sectors, with the first exhibiting the usual pattern of a spontaneously broken chiral symmetry, and the second exhibiting an additional, unbroken symmetry and parity doubling. The first sector includes the Goldstone bosons and other states such as massive scalar partners. The second includes a parity-degenerate vector and axial vector along with other possible parity partners. We note that if such a near-critical theory describes symmetry breaking in the electroweak theory, the additional symmetry suppresses the contribution of the parity-doubled sector to the S parameter.

Quantum Hall Plateau Transitions in Disordered Superconductors

Abstract: We study a delocalization transition for noninteracting quasiparticles moving in two dimensions, which belongs to a new symmetry class. This symmetry class can be realized in a dirty, gapless superconductor in which time-reversal symmetry for orbital motion is broken, but spin-rotation symmetry is intact. We find a direct transition between two insulating phases with quantized Hall conductances of zero and two for the conserved quasiparticles. The energy of the quasiparticles acts as a relevant symmetry-breaking field at the critical point, which splits the direct transition into two conventional plateau transitions.

Conventional mechanisms for exotic superconductivity

Abstract: We consider the pairing state due to the usual BCS mechanism in substances of cubic and hexagonal symmetry where the Fermi surface forms pockets around several points of high symmetry. We find that the symmetry imposed on the multiple pocket positions could give rise to a multidimensional nontrivial superconducting order parameter. The time-reversal symmetry in the pairing state is broken. We suggest several candidate substances where such ordering may appear, and discuss means by which such a phase may be identified.

Universality and the magnetic catalysis of chiral symmetry breaking

Abstract: The hypothesis that the magnetic catalysis of chiral symmetry breaking is due to interactions of massless fermions in their lowest Landau level is examined in the context of chirally symmetric models with short ranged interactions. It is argued that, when the magnetic field is sufficiently large, even an infinitesimal attractive interaction in the appropriate channel will break chiral symmetry. {copyright} {ital 1999} {ital The American Physical Society}

Laws of nature, probability and time symmetry breaking

Abstract: The work of the Austin-Brussels group on the microscopic origin of irreversibility is described. Using extensions of the traditional Hilbert space and Poincare's nonintegrability, we obtain new formulations of laws of dynamics which can be expressed only in terms of probabilities (and not in terms of trajectories or wave functions) and which include time symmetry breaking.

Dynamical chiral symmetry breaking in QED in a magnetic field: Toward exact results

Abstract: We describe an (first, to the best of our knowledge) essentially soluble example of dynamical symmetry breaking phenomenon in a $(3+1)$-dimensional gauge theory without fundamental scalar fields: QED in a constant magnetic field.

Anomalous magnetic moment of quarks

Abstract: In the case of massless current quarks we find that the breaking of chiral symmetry usually triggers the generation of an anomalous magnetic moment for the quarks. We show that the kernel of the Ward identity for the vector vertex yields an important contribution. We compute the anomalous magnetic moment in several quark models. The results show that it is hard to escape a measurable anomalous magnetic moment for the quarks in the case of spontaneous chiral symmetry breaking.

Matter Representations and Gauge Symmetry Breaking via Compactified Space

Abstract: We study dynamical gauge symmetry breaking via compactified space in the framework of SU(N )gauge theory in M d−1 × S 1 (d =4 , 5, 6)space-time. In particular, we study in detail the gauge symmetry breaking in SU(2)and SU(3)gauge theories when the models contain both fundamental and adjoint matter. As a result, we find that any pattern of gauge symmetry breaking can be realized by selecting an appropriate set of numbers (Nf ,N ad)in these cases. This is achieved without tuning boundary conditions of the matter fields. As a by-product, in some cases we obtain an effective potential which has no curvature at the minimum, thus leading to massless Higgs scalars, irrespective of the size of the compactified space.

Point-group symmetries in electromagnetic scattering

Abstract: A relation is developed between point-group symmetries of light-scattering particles and symmetry relations for the electromagnetic scattering solution in the T-matrix formulation. A systematic derivation of a representation of symmetry operations is presented in the vector space on which the T matrix operates. From this the set of symmetry relations of the T matrix is obtained for various point groups. As examples several symmetry groups relevant to modeling atmospheric particles are treated, such as the K group of spherical symmetry, the C∞v group of axial symmetry, and the D∞h group of dihedral axial symmetry. The D∞h symmetry relations for the T matrix in spheroidal coordinates (denoted by script font) are also derived. Previously known symmetry relations of the T matrix can be verified, and new relations are found for DNh symmetry, i.e., for the important case of particles with dihedral symmetry and an N-fold axis of rotation.

Flavor universal dynamical electroweak symmetry breaking

Abstract: The top condensate seesaw mechanism of Dobrescu and Hill allows electroweak symmetry to be broken while deferring the problem of flavor to an electroweak singlet, massive sector. We provide an extended version of the singlet sector that naturally accommodates realistic masses for all the standard model fermions, which play an equal role in breaking electroweak symmetry. The models result in a relatively light composite Higgs sector with masses typically in the range of (400{endash}700) GeV. In more complete models the dynamics will presumably be driven by a broken gauged family or flavor symmetry group. As an example of the higher scale dynamics a fully dynamical model of the quark sector with a GIM mechanism is presented, based on an earlier top condensation model of King using broken family gauge symmetry interactions (that model was itself based on a technicolor model of Georgi). The crucial extra ingredient is a reinterpretation of the condensates that form when several gauge groups become strong close to the same scale. A related technicolor model of Randall which naturally includes the leptons too may also be adapted to this scenario. We discuss the low energy constraints on the massive gauge bosons and scalars of these modelsmore » as well as their phenomenology at the TeV scale. thinsp thinsp {copyright} {ital 1999} {ital The American Physical Society}« less

Parity and CT Realization in QCD

Abstract: We show that an essential assumption in the Vafa and Witten's theorem on P and CT realization in vector-like theories, the existence of a free energy density in Euclidean space in the presence of any external hermitian symmetry breaking source, does not apply if the symmetry is spontaneously broken. The assumption that the free energy density is well defined requires the previous assumption that the symmetry is realized in the vacuum. Even if Vafa and Witten's conjecture is plausible, actually a theorem is still lacking.

Effective Field Theory Approach to Ferromagnets and Antiferromagnets in Crystalline Solids

Abstract: We present a systematic construction of effective Lagrangians for the low energy and momentum region of ferromagnetic and antiferromagnetic spin waves in crystalline solids. We fully exploit the spontaneous symmetry breaking pattern SU(2)→U(1), the fact that spin waves are its associated Goldstone modes, the crystallographic space group and time reversal symmetries. We show how to include explicit SU(2) breaking terms due to spin-orbit and magnetic dipole interactions. The coupling to electromagnetic fields is also discussed in detail. For definiteness we work with the space group and present our results to next to leading order.

Translational symmetry breaking in two-dimensional antiferromagnets and superconductors

Abstract: It was argued many years ago that translational symmetry breaking due to the appearance of spin-Peierls ordering (or bond-charge stripe order) is a fundamental property of the quantum paramagnetic states of a large class of square lattice antiferromagnets. Recently, such states were shown to be a convenient point of departure for studying translational symmetry breaking in doped antiferromagnets: these results are briefly reviewed here with an emphasis on experimental implications. In the presence of stronger frustration, it was also argued that the insulating antiferromagnet can undergo a transition to a deconfined state with no lattice symmetry breaking. This transition is described by a fully-frustrated Ising model in a transverse field: details of this earlier derivation of the Ising model are provided here--this is motivated by the reappearance of the same Ising model in a recent study of the competition between antiferromagnetism and d-wave superconductivity by Senthil and Fisher (cond-mat/9910224).

Anomalous Chiral Symmetry Breaking above the QCD Phase Transition

Abstract: We study the anomalous breaking of ${\mathrm{U}}_{A}(1)$ symmetry just above the QCD phase transition for zero and two flavors of quarks, using a staggered fermion, lattice discretization. The properties of the QCD phase transition are expected to depend on the degree of ${\mathrm{U}}_{A}(1)$ symmetry breaking in the transition region. For the physical case of two flavors, we carry out extensive simulations on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}4$ lattice, measuring a difference in susceptibilities which is sensitive to ${\mathrm{U}}_{A}(1)$ symmetry and which avoids many of the staggered fermion discretization difficulties. The results suggest that anomalous effects are at or below the 15% level.

Symmetry groups and separation of variables of a class of nonlinear diffusion-convection equations

Abstract: In this paper, a class of nonlinear diffusion-convection equations, ut = (D(u)uxn)x+P(u)ux , which has quite a large number of physical applications, is analysed by using symmetry group methods which include the classical method, the potential symmetry method and the generalized conditional symmetry method. A complete classification of the functional forms of the diffusion and convection coefficients is presented when the equation admits Lie's point symmetry groups and potential symmetry groups. The separation of variables for the equation is investigated using the generalized conditional symmetry approach. For some interesting cases, exact solutions using the method of separation of variables are discussed in detail.

Why all crystals need not be bcc : symmetry breaking at the liquid-solid transition revisited

Abstract: Alexander and McTague [Phys.Rev. Lett. 41, 702 (1978)] argued that if there is a spinodal point associated with the liquid-solid transition in a fluid of spherically symmetric particles, the bcc phase will be uniquely favored as the only accessible symmetry breaking structure that forms a regular three-dimensional lattice. By reconsidering their analysis in the framework of density-functional theory, we show that at a liquid-solid spinodal in fact many other solid stuctures also are simultaneously accessible, among them the fcc structure. Nevertheless, the bcc structure is still shown to be special, as, independent of the details of the interaction, the free energy of the unstable bcc phase close to the spinodal is always lower than that of the other solidlike structures. We illustrate our general results by explicit calculations on a toy model, the "Onsager solid." This simple model also indicates that the ultimately stable crystal phase, which, as usual for sufficiently steep repulsive forces, turns out to be fcc, is dictated by properties of the free energy that cannot be obtained perturbatively starting from the spinodal point.