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Simon Hands

Publications and source records attributed to Simon Hands.

At least 127 records · Page 7Linked to original sources

The Phase Diagram of QCD

I use simple thermodynamic reasoning to argue that at temperatures of order a trillion kelvin, QCD, the theory which describes strongly interacting particles such as protons and neutrons under normal conditions, undergoes a phase transition to a plasma of more elementary constituents called quarks and gluons. I review what is known about the plasma phase both from theoretical calculations and from experiments involving the collisions of large atomic nuclei moving at relativistic speeds. Finally I consider the behaviour of nuclear material under conditions of extreme density, and discuss possible exotic phenomena such as quark matter and color superconductivity.

physics.ed-ph↗

Numerical Study of dense adjoint 2-color matter

We study the global symmetries of SU(2) gauge theory with N flavors of staggered fermions in the presence of a chemical potential. We motivate the special interest of the case N=1 (staggered) with fermions in the adjoint representation of the gauge group. We present results from numerical simulations with both hybrid Monte Carlo and the Two-Step Multi-Bosonic algorithm.

hep-lat↗

Critical Behaviour in the Dense Planar NJL Model

We present results of a Monte Carlo simulation of a 2+1 dimensional Nambu - Jona-Lasinio model including diquark source terms. A diquark condensate is measured as a function of source strength j. In the vacuum phase vanishes linearly with j as expected, but simulations in a region with non-zero baryon density suggest a power-law scaling and hence a critical system for all mu > mu_c. There is no diquark condensation signalling superfluidity. Comparisons are drawn with known results in two dimensional theories, and with the pseudogap phase in cuprate superconductors. We also measure the dispersion relation E(k) for fermionic excitations, and find results consistent with a sharp Fermi surface. Any superfluid gap Delta is constrained to be much less than the constituent quark mass scale Sigma_0.

hep-lat↗

The Phase Diagram of the Three Dimensional Thirring Model

We present Monte Carlo simulation results for the three dimensional Thirring model on moderate sized lattices using a hybrid molecular dynamics algorithm which permits an odd or non-integer number Nf of fermion flavors. We find a continuous chiral symmetry breaking transition for Nf approximately equal to 3 with critical exponents consistent with expectations from previous studies. For Nf=5 the order of the transition is difficult to determine on the lattice sizes explored. We present a phase diagram for the model in the (1/g^2,Nf) plane and contrast our findings with expectations based on approximate solutions of the continuum Schwinger-Dyson equations.

hep-lat↗

Diquark Condensation in Dense Matter - A Lattice Perspective

We review efforts to study, using the methods of lattice field theory, the phenomenon of diquark condensation via BCS pairing at a Fermi surface, which has been proposed as a mechanism for color superconductivity in dense quark matter. The particular models studied are the Gross-Neveu model and SU(2) lattice gauge theory; in both cases evidence for superfluidity at high density is presented. The behaviour expected for quarks in both fundamental and adjoint representations of SU(2) is contrasted.

hep-lat↗

Symmetries and spectrum of SU(2) Lattice Gauge Theory at finite chemical potential

We study SU(2) Lattice Gauge Theory with dynamical fermions at non-zero chemical potential $μ$. The symmetries special to SU(2) for staggered fermions on the lattice are discussed explicitly and their relevance to spectroscopy and condensates at non-zero chemical potential are considered. Using the molecular dynamics algorithm on small lattices we find qualitative changes in the theory's spectroscopy at small and large values of $μ$. This preliminary study should lay the groundwork for future large scale simulations.

hep-lat↗

Chiral Symmetry Restoration and Realisation of the Goldstone Mechanism in the U(1) Gross-Neveu Model at Non-Zero Chemical Potential

We simulate the Gross-Neveu model in 2+1 dimensions at nonzero baryon density (chemical potential mu =/= 0). It is possible to formulate this model with a real action and therefore to perform standard hybrid Monte Carlo simulations with mu =/= 0 in the functional measure. We compare the physical observables from these simulations with simulations using the Glasgow method where the value of mu in the functional measure is fixed at a value mu_upd. We find that the observables are sensitive to the choice of mu_upd. We consider the implications of our findings for Glasgow method QCD simulations at mu =/= 0. We demonstrate that the realisation of the Goldstone mechanism in the Gross-Neveu model is fundamentally different from that in QCD. We find that this difference explains why there is an unphysical transition in QCD simulations at mu =/= 0 associated with the pion mass scale whereas the transition in the Gross-Neveu model occurs at a larger mass scale and is therefore consistent with theoretical predictions. We note classes of theories which are exceptions to the Vafa-Witten theorem which permit the possibility of formation of baryon number violating diquark condensates.

hep-lat↗

Measuring Diquark Condensation in Lattice Simulations of Dense Matter

We discuss general aspects of the possibility of Bose condensation of diquark pairs in systems of dense matter. Lattice field theory simulations are presented for model four-fermion theories which are expected to manifest the phenomenon, and results from measurements of both diquark two-point and one-point functions presented. Whilst initial results are promising, there remain systematic effects needing to be understood.

hep-lat↗

Two Colours QCD at Nonzero Chemical Potential

We identify the Goldstone modes appropriate to the low and high density phases of SU(2) lattice gauge theory with staggered fermions. We present hybrid Monte Carlo simulation results for susceptibilities on a 6^4 lattice at beta=1.5, m=0.05. We specify how to implement a diquark source term in a lattice simulation and present first measurements of the lattice diquark condensate as a function of the diquark source.

hep-lat↗

Lattice Simulation of Diquark Condensation in Dense Matter

We present results of a Monte Carlo simulation of a three dimensional Gross-Neveu model with SU(2)xSU(2) chiral symmetry at non-zero baryon chemical potential mu, corresponding to non-zero baryon density. For mu sufficiently large there is a sharp transition between a phase where the chiral symmetry is broken by a condensate and one where the global U(1) baryon number symmetry appears to be broken by a scalar diquark condensate . There is also tentative evidence for the formation of a weaker pseudoscalar diquark condensate in the high density phase, which violoates parity.

hep-lat↗

Four Fermion Models at Non-Zero Density

I review the properties of the three-dimensional Gross-Neveu model formulated with non-zero chemical potential and temperature, focussing on results obtained by lattice Monte Carlo simulation.

hep-lat↗

Magnetic Monopoles as Agents of Chiral Symmetry Breaking in U(1) Lattice Gauge Theory

We present results suggesting that magnetic monopoles can account for chiral symmetry breaking in abelian gauge theory. Full U(1) configurations from a lattice simulation are factorized into magnetic monopole and photon contributions. The expectation is computed using the monopole configurations and compared to results for the full U(1) configurations. It is shown that excellent agreement between the two values of is obtained if the effect of photons, which "dress" the composite operator psibarpsi, is included. This can be estimated independently by measurements of the physical fermion mass in the photon background.

hep-lat↗

Log Triviality in the Nambu -- Jona-Lasinio Model

Results are presented from a Monte Carlo simulation of the Nambu -- Jona-Lasinio model with SU(2)xSU(2) chiral symmetry and N_f=2 flavors of fermion. We show that fits to the equation of state are sensitive to the shape and extent of the assumed scaling region; the best fits favour a triviality scenario predicted by the large-N_f approximation, in which the scalar degrees of freedom are fermion -- anti-fermion composites with wavefunction renormalisation constant vanishing logarithmically in the continuum limit.

hep-lat↗

Fixed Point Four-Fermi Theories

I review dynamical chiral symmetry breaking in four-fermi models, including results of Monte Carlo simulations with dynamical fermions. For 2<d<4, where the phase transition defines an ultraviolet fixed point of the renormalisation group, the continuum theory may either be describable using the large-N_f expansion, as in the case of the Gross-Neveu model, or be intrinsically non-perturbative, as in the case of the Thirring model. For d=4, the models are trivial and are described by a mean field equation of state with logarithmic corrections to scaling, which may nonetheless define new universality classes distinct from those of ferromagnetism.

hep-lat↗

Logarithmic Corrections to the Equation of State in the SU(2)xSU(2) Nambu - Jona-Lasinio Model

We present results from a Monte Carlo simulation of the Nambu - Jona-Lasinio model, with continuous SU(2)xSU(2) chiral symmetry, in four Euclidean dimensions. Different model equations of state, corresponding to different theoretical scenarios, are tested against the order parameter data. The results are sensitive to necessary assumptions about the shape and extent of the scaling region. Our best fits favour a trivial scenario in which the logarithmic corrections are qualitatively similar to those predicted by the large N_f approximation. This is supported by a separate analysis of finite volume corrections for data taken directly in the chiral limit.

hep-lat↗

Monte Carlo Study of the 3D Thirring Model

I review three different non-perturbative approaches to the three dimensional Thirring model: the 1/N_f expansion, Schwinger-Dyson equations, and Monte Carlo simulation. Simulation results are presented to support the existence of a non-perturbative fixed point at a chiral symmetry breaking phase transition for N_f=2 and 4, but not for N_f=6. Spectrum calculations for $N_f=2$ reveal conventional level ordering near the transition.

hep-lat↗

Monte Carlo Simulation of the Three Dimensional Thirring Model

We study the Thirring model in three spacetime dimensions, by means of Monte Carlo simulation on lattice sizes 8^3 and 12^3, for numbers of fermion flavors N_f=2,4,6. For sufficiently strong interaction strength, we find that spontaneous chiral symmetry breaking occurs for N_f=2,4, in accordance with the predictions of the Schwinger-Dyson approach. The phase transitions which occur are continuous and with critical scaling behaviour depending on N_f. For N_f=6 our results are preliminary, and no firm conclusions about the existence or otherwise of chiral symmetry breaking are possible

hep-lat↗

Electromagnetic Self-Duality in a Lattice Model

We formulate a Euclidean lattice theory of interacting elementary spin-half electric and magnetic charges, which we refer to as electrons and magnetic monopoles respectively. The model uses the polymer representation of the fermion determinant, and exhibits a self-dual symmetry provided electric charge $e$ and magnetic charge $g$ obey the minimal Dirac quantisation condition $eg=2π$. In a hopping parameter expansion at lowest order, we show that virtual electron and monopole loops contribute radiative corrections of opposite sign to the photon propagator. We argue that in the limit $e\to0$, fermion mass $μ\to0$, the model describes QED together with strongly interacting monopoles whose chiral symmetry is spontaneously broken. Prospects for the existence of an interacting continuum limit at the self-dual point $e=g$ are discussed.

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