Tethered Monte Carlo: computing the effective potential without critical slowing down

We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two-dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L = 1024.

Tethered Monte Carlo: computing the effective potential without critical slowing down

We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two-dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L = 1024.

Characterizing the satellites of massive galaxies up to z ∼ 2: young populations to build the outskirts of nearby massive galaxies

The accretion of minor satellites is currently proposed as the most likely mechanism to explain the significant size evolution of the massive galaxies during the last ∼10 Gyr. In this paper, we investigate the rest-frame colours and the average stellar ages of satellites found around massive galaxies (M_star ∼ 10^11 M_⊙) since z ∼ 2. We find that the satellites have bluer colours than their central galaxies. When exploring the stellar ages of the galaxies, we find that the satellites have similar ages to the massive galaxies that host them at high redshifts, while at lower redshifts they are, on average, ≳1.5 Gyr younger. If our satellite galaxies create the envelope of nearby massive galaxies, our results would be compatible with the idea that the outskirts of those galaxies are slightly younger, metal-poorer and with lower [α/Fe] abundance ratios than their inner regions.

Satellites around massive galaxies since z∼ 2

The accretion of minor satellites has been postulated as the most likely mechanism to explain the significant size evolution of massive galaxies over cosmic time. Using a sample of 629 massive (M_star~ 10^11 M_⊙) galaxies from the near-infrared Palomar/DEEP-2 survey, we explore what fraction of these objects have satellites with 0.01 < M_sat/M_central < 1 (1:100) up to z= 1 and what fraction have satellites with 0.1 < M_sat/M_central < 1 (1:10) up to z= 2 within a projected radial distance of 100 kpc. We find that the fraction of massive galaxies with satellites, after background correction, remains basically constant and close to 30 per cent for satellites with a mass ratio down to 1:100 up to z= 1, and close to 15 per cent for satellites with a 1:10 mass ratio up to z= 2. The family of spheroid-like massive galaxies presents a 2–3 times larger fraction of objects with satellites than the group of disc-like massive galaxies. A crude estimation of the number of 1:3 mergers a massive spheroid-like galaxy has experienced since z~2 is around 2. For a disc-like galaxy this number decreases to ~1.