Numerical Studies of the two-leg Hubbard ladder

The Hubbard model on a two-leg ladder structure has been studied by a combination of series expansions at T=0 and the density-matrix renormalization group. We report results for the ground state energy $E_0$ and spin-gap $\Delta_s$ at half-filling, as well as dispersion curves for one and two-hole excitations. For small $U$ both $E_0$ and $\Delta_s$ show a dramatic drop near $t/t_{\perp}\sim 0.5$, which becomes more gradual for larger $U$. This represents a crossover from a "band insulator" phase to a strongly correlated spin liquid. The lowest-lying two-hole state rapidly becomes strongly bound as $t/t_{\perp}$ increases, indicating the possibility that phase separation may occur. The various features are collected in a "phase diagram" for the model.Comment: 10 figures, revte

Critical domain-wall dynamics of model B

With Monte Carlo methods, we simulate the critical domain-wall dynamics of model B, taking the two-dimensional Ising model as an example. In the macroscopic short-time regime, a dynamic scaling form is revealed. Due to the existence of the quasi-random walkers, the magnetization shows intrinsic dependence on the lattice size $L$. A new exponent which governs the $L$-dependence of the magnetization is measured to be $\sigma=0.243(8)$.Comment: 10pages, 4 figure

Networking Effects on Cooperation in Evolutionary Snowdrift Game

The effects of networking on the extent of cooperation emerging in a competitive setting are studied. The evolutionary snowdrift game, which represents a realistic alternative to the well-known Prisoner's Dilemma, is studied in the Watts-Strogatz network that spans the regular, small-world, and random networks through random re-wiring. Over a wide range of payoffs, a re-wired network is found to suppress cooperation when compared with a well-mixed or fully connected system. Two extinction payoffs, that characterize the emergence of a homogeneous steady state, are identified. It is found that, unlike in the Prisoner's Dilemma, the standard deviation of the degree distribution is the dominant network property that governs the extinction payoffs.Comment: Changed conten

Cosmic clocks: A Tight Radius - Velocity Relationship for HI-Selected Galaxies

HI-Selected galaxies obey a linear relationship between their maximum detected radius Rmax and rotational velocity. This result covers measurements in the optical, ultraviolet, and HI emission in galaxies spanning a factor of 30 in size and velocity, from small dwarf irregulars to the largest spirals. Hence, galaxies behave as clocks, rotating once a Gyr at the very outskirts of their discs. Observations of a large optically-selected sample are consistent, implying this relationship is generic to disc galaxies in the low redshift Universe. A linear RV relationship is expected from simple models of galaxy formation and evolution. The total mass within Rmax has collapsed by a factor of 37 compared to the present mean density of the Universe. Adopting standard assumptions we find a mean halo spin parameter lambda in the range 0.020 to 0.035. The dispersion in lambda, 0.16 dex, is smaller than expected from simulations. This may be due to the biases in our selection of disc galaxies rather than all halos. The estimated mass densities of stars and atomic gas at Rmax are similar (~0.5 Msun/pc^2) indicating outer discs are highly evolved. The gas consumption and stellar population build time-scales are hundreds of Gyr, hence star formation is not driving the current evolution of outer discs. The estimated ratio between Rmax and disc scale length is consistent with long-standing predictions from monolithic collapse models. Hence, it remains unclear whether disc extent results from continual accretion, a rapid initial collapse, secular evolution or a combination thereof.Comment: 14 pages, 7 figures, 3 in colour. Published in MNRAS. This v2 corrects wrong journal in the references section (all instances of "Astrophysics and Space Sciences" should have been ApJ). The Posti+2017 has also been updated. An erratum has been submitted to MNRA

Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice

We investigate ground state and finite temperature properties of the half-filled Hubbard model on a honeycomb lattice using quantum monte carlo and series expansion techniques. Unlike the square lattice, for which magnetic order exists at T=0 for any non-zero $U$, the honeycomb lattice is known to have a semi-metal phase at small $U$ and an antiferromagnetic one at large $U$. We investigate the phase transition at T=0 by studying the magnetic structure$and compressibility using quantum monte carlo simulations and by calculating the sublattice magnetization, uniform susceptibility, spin-wave and single hole ordered phase. Our results are consistent with a single continuous transition at$U_c/t$in the range 4-5. Finite temperature signatures of this phase transition are seen in the behavior of the specific heat,$C(T)$, which changes from a two-peaked structure for$U>U_c$to a one-peaked structure for$U < U_c$. Furthermore, the$U$dependence of the low temperature coefficient of$C(T)$exhibits an anomaly at$U \approx U_c$.Comment: 11 pages, 19 figure