A Proposal of a Renormalization Group Transformation for Lattice Field Theories

We propose a new Real Space Renormalization Group transformation useful for Monte Carlo calculations in theories with global or local symmetries. From relaxation arguments we define the block-spin transformation with two tunable free parameters, adapted to the system's action. Varying them it is possible to place the fixed point very close to the simulation point. We show how the method works in a simple model with global symmetry: the three dimensional XY model.Comment: 26 pages, uuencoded compressed postscript single file, 8 figures include

Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions

We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out in the citizen supercomputer Ibercivis. Upon dilution, the pure model's first-order transition becomes of the second-order at a tricritical point. We compute accurately the critical exponents at the tricritical point. As expected from the Cardy-Jacobsen conjecture, they are compatible with their Random Field Ising Model counterpart. The conclusion is further reinforced by comparison with older data for the Potts model with four states.Comment: Final version. 9 pages, 9 figure

The out-equilibrium 2D Ising spin glass: almost, but not quite, a free-field theory

We consider the spatial correlation function of the two-dimensional Ising spin glass under out-equilibrium conditions. We pay special attention to the scaling limit reached upon approaching zero temperature. The field-theory of a non-interacting field makes a surprisingly good job at describing the spatial shape of the correlation function of the out-equilibrium Edwards-Anderson Ising model in two dimensions.Comment: 20 pages + 5 Figure

Effect of Dilution on First Order Transitions: The Three Dimensional Three States Potts Model

We have studied numerically the effect of quenched site dilution on a first order phase transition in three dimensions. We have simulated the site diluted three states Potts model studying in detail the second order region of its phase diagram. We have found that the $\nu$ exponent is compatible with the one of the three dimensional diluted Ising model whereas the $\eta$ exponent is definitely different.Comment: RevTex. 6 pages and 6 postscript figure

Tempering Dynamics and Relaxation Times in the 3D3D Ising Model

We discuss the tempering Monte Carlo method, and its critical slowing down in the $3d$ Ising model. We show that at $T_c$ the tempering does not change the critical slowing down exponent $z$. We also discuss the exponential slowing down for the transition from the plus to the minus state in the cold phase, and we show that tempering reduces it to a power law slowing down. We discuss the relation of the flip-flop rate to the surface tension for the local dynamical schemes.Comment: 10 pages, compressed ps-file (uufiles

Microcanonical finite-size scaling in specific heat diverging 2nd order phase transitions

A Microcanonical Finite Site Ansatz in terms of quantities measurable in a Finite Lattice allows to extend phenomenological renormalization (the so called quotients method) to the microcanonical ensemble. The Ansatz is tested numerically in two models where the canonical specific-heat diverges at criticality, thus implying Fisher-renormalization of the critical exponents: the 3D ferromagnetic Ising model and the 2D four-states Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows to simulate systems as large as L=1024 (Potts) or L=128 (Ising). The quotients method provides extremely accurate determinations of the anomalous dimension and of the (Fisher-renormalized) thermal $\nu$ exponent. While in the Ising model the numerical agreement with our theoretical expectations is impressive, in the Potts case we need to carefully incorporate logarithmic corrections to the microcanonical Ansatz in order to rationalize our data.Comment: 13 pages, 8 figure

Comment on "Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model"

A recent interesting paper [Yucesoy et al. Phys. Rev. Lett. 109, 177204 (2012), arXiv:1206:0783] compares the low-temperature phase of the 3D Edwards-Anderson (EA) model to its mean-field counterpart, the Sherrington-Kirkpatrick (SK) model. The authors study the overlap distributions P_J(q) and conclude that the two models behave differently. Here we notice that a similar analysis using state-of-the-art, larger data sets for the EA model (generated with the Janus computer) leads to a very clear interpretation of the results of Yucesoy et al., showing that the EA model behaves as predicted by the replica symmetry breaking (RSB) theory.Comment: Version accepted for publication in PRL. 1 page, 1 figur

Study of star-forming galaxies in SDSS up to redshift 0.4: I. Metallicity evolution

The chemical composition of the gas in galaxies versus cosmic time provides a very important tool for understanding galaxy evolution. Although there are many studies at high redshift, they are rather scarce at lower redshifts. However, low redshift studies can provide important clues about the evolution of galaxies, furnishing the required link between local and high redshift universe. In this work we focus on the metallicity of the gas of star-forming galaxies at low redshift, looking for signs of chemical evolution. To analyze the metallicity contents star-forming galaxies of similar luminosities and masses at different redshifts. With this purpose, we present a study of the metallicity of relatively massive (log(M_star/M_sun)>10.5) star forming galaxies from SDSS--DR5 (Sloan Digital Sky Survey--Data Release 5), using different redshift intervals from 0.04 to 0.4. We used data processed with the STARLIGHT spectral synthesis code, correcting the fluxes for dust extinction, estimating metallicities using the R_23 method, and segregating the samples with respect to the value of the [NII]6583/[OII]3727 line ratio in order to break the R_23 degeneracy selecting the upper branch. We analyze the luminosity and mass-metallicity relations, and the effect of the Sloan fiber diameter looking for possible biases. By dividing our redshift samples in intervals of similar magnitude and comparing them, significant signs of metallicity evolution are found. Metallicity correlates inversely with redshift: from redshift 0 to 0.4 a decrement of ~0.1 dex in 12+log(O/H) is found.Comment: 11 pages, 9 figures, Accepted for publication in A&

An experiment-oriented analysis of 2D spin-glass dynamics: a twelve time-decades scaling study

Recent high precision experimental results on spin-glass films ask for a detailed understanding of the domain-growth dynamics of two-dimensional spin glasses. To achieve this goal, we numerically simulate the out-equilibrium dynamics of the Ising spin glass for a time that spans close to twelve orders of magnitude (from picoseconds to order of a second), in systems large enough to avoid finite-size effects. We find that the time-growth of the size of the glassy domains is excellently described by a single scaling function. A single time-scale $\tau(T)$ controls the dynamics. $\tau(T)$ diverges upon approaching the $T=0$ critical point. The divergence of $\tau(T\to 0)$ is Arrhenius-like, with a barrier height that depends very mildly on temperature. The growth of this barrier-height is best described by critical dynamics. As a side product we obtain an impressive confirmation of universality of the equilibrium behavior of two-dimensional spin-glasses.Comment: 21 pages, 9 figures. Updated references. Added DOI and Journal re

Small-angle neutron scattering and Molecular Dynamics structural study of gelling DNA nanostars

DNA oligomers with properly designed sequences self-assemble into well defined constructs. Here, we exploit this methodology to produce bulk quantities of tetravalent DNA nanostars (each one composed by 196 nucleotides) and to explore the structural signatures of their aggregation process. We report small-angle neutron scattering experiments focused on the evaluation of both the form factor and the temperature evolution of the scattered intensity at a nano star concentration where the system forms a tetravalent equilibrium gel. We also perform molecular dynamics simulations of one isolated tetramer to evaluate the form factor theoretically, without resorting to any approximate shape. The numerical form factor is found to be in very good agreement with the experimental one. Simulations predict an essentially temperature independent form factor, offering the possibility to extract the effective structure factor and its evolution during the equilibrium gelation.Comment: 9 pages, 5 figure