Hybrid Monte-Carlo simulation of interacting tight-binding model of graphene

In this work, results are presented of Hybrid-Monte-Carlo simulations of the tight-binding Hamiltonian of graphene, coupled to an instantaneous long-range two-body potential which is modeled by a Hubbard-Stratonovich auxiliary field. We present an investigation of the spontaneous breaking of the sublattice symmetry, which corresponds to a phase transition from a conducting to an insulating phase and which occurs when the effective fine-structure constant $\alpha$ of the system crosses above a certain threshold $\alpha_C$. Qualitative comparisons to earlier works on the subject (which used larger system sizes and higher statistics) are made and it is established that $\alpha_C$ is of a plausible magnitude in our simulations. Also, we discuss differences between simulations using compact and non-compact variants of the Hubbard field and present a quantitative comparison of distinct discretization schemes of the Euclidean time-like dimension in the Fermion operator.Comment: 7 pages, 1 figure, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Spectrum of QCD at Finite Isospin Density

We study the phase diagram of QCD at finite isospin density using two flavors of staggered quarks. We investigate the low temperature region of the phase diagram where we find a pion condensation phase at high chemical potential. We started a basic analysis of the spectrum at finite isospin density. In particular, we measured pion, rho and nucleon masses inside and outside of the pion condensation phase. In agreement with previous studies in two-color QCD at finite baryon density we find that the Polyakov loop does not depend on the density in the staggered formulation.Comment: 8 pages, 7 figures, proceedings of Lattice2017, Granada, Spai

Effective potential for SU(2) Polyakov loops and Wilson loop eigenvalues

We simulate SU(2) gauge theory at temperatures ranging from slightly below $T_c$ to roughly $2T_c$ for two different values of the gauge coupling. Using a histogram method, we extract the effective potential for the Polyakov loop and for the phases of the eigenvalues of the thermal Wilson loop, in both the fundamental and adjoint representations. We show that the classical potential of the fundamental loop can be parametrized within a simple model which includes a Vandermonde potential and terms linear and quadratic in the Polyakov loop. We discuss how parametrizations for the other cases can be obtained from this model.Comment: 16 pages, 39 figure

On the universal critical behavior in 3-flavor QCD

We analyze the universal critical behavior at the chiral critical point in QCD with three degenerate quark masses. We confirm that this critical point lies in the universality class of the three dimensional Ising model. The symmetry of the Ising model, which is Z(2), is not directly realized in the QCD Hamiltonian. After making an ansatz for the magnetization- and energy-like operators as linear admixtures of the chiral condensate and the gluonic action, we determine several non-universal mixing and normalization constants. These parameters determine an unambiguous mapping of the critical behavior in QCD to that of the 3d-Ising model. We verify its validity by showing that the thus obtained orderparameter scales in accordance with the magnetic equation of state of the 3d-Ising model.Comment: 7 pages, contribution to Lattice 2011 proceeding

Lattice simulation of a center symmetric three-dimensional effective theory for SU(2) Yang-Mills

We perform simulations of an effective theory of SU(2) Wilson lines in three dimensions. Our action includes a kinetic term, the one-loop perturbative potential for the Wilson line, a non-perturbative "fuzzy-bag" contribution and spatial gauge fields. We determine the phase diagram of the theory and confirm that, at moderately weak coupling, the non-perturbative term leads to eigenvalue repulsion in a finite region above the deconfining phase transition.Comment: To appear in the proceedings of "Strong and Electroweak Matter", Amsterdam, the Netherlands, August 26-29, Nucl. Phys. A, in prin

Low-metallicity star formation: Relative impact of metals and magnetic fields

Low-metallicity star formation poses a central problem of cosmology, as it determines the characteristic mass scale and distribution for the first and second generations of stars forming in our Universe. Here, we present a comprehensive investigation assessing the relative impact of metals and magnetic fields, which may both be present during low-metallicity star formation. We show that the presence of magnetic fields generated via the small-scale dynamo stabilises the protostellar disc and provides some degree of support against fragmentation. In the absence of magnetic fields, the fragmentation timescale in our model decreases by a factor of ~10 at the transition from Z=0 to Z>0, with subsequently only a weak dependence on metallicity. Similarly, the accretion timescale of the cluster is set by the large-scale dynamics rather than the local thermodynamics. In the presence of magnetic fields, the primordial disc can become completely stable, therefore forming only one central fragment. At Z>0, the number of fragments is somewhat reduced in the presence of magnetic fields, though the shape of the mass spectrum is not strongly affected in the limits of the statistical uncertainties. The fragmentation timescale, however, increases by roughly a factor of 3 in the presence of magnetic fields. Indeed, our results indicate comparable fragmentation timescales in primordial runs without magnetic fields and Z>0 runs with magnetic fields.Comment: MNRAS in pres