Searcharxiv⌕ Search

arXiv subjects

V. Martin-Mayor

Publications and source records attributed to V. Martin-Mayor.

At least 55 records · Page 3Linked to original sources
arXiv2013

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.

cond-mat.dis-nn↗
arXiv2012

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.

cond-mat.dis-nn↗
arXiv2012

The correspondence between long-range and short-range spin glasses

We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power sigma of the distance. We show that there is a value of sigma of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions. We also study a value of sigma for which we find the critical behavior to be compatible with that of the three dimensional model, though we have much less precision than in the four-dimensional case.

cond-mat.dis-nn↗
arXiv2012

Neutron scattering experiments and simulations near the magnetic percolation threshold of Fe_x Zn_{1-x} F_2

The low temperature excitations in the anisotropic antiferromagnetic Fe_{1-x} Zn_x F_2 for x=0.25 and 0.31, at and just above the magnetic percolation threshold concentration x_p=0.25, were measured using inelastic neutron scattering. The excitations were simulated for x=0.31 using a localized, classical excitation model, which accounts well for the energies and relative intensities of the excitations observed in the scattering experiments.

cond-mat.str-el↗
arXiv2012

Reconfigurable computing for Monte Carlo simulations: results and prospects of the Janus project

We describe Janus, a massively parallel FPGA-based computer optimized for the simulation of spin glasses, theoretical models for the behavior of glassy materials. FPGAs (as compared to GPUs or many-core processors) provide a complementary approach to massively parallel computing. In particular, our model problem is formulated in terms of binary variables, and floating-point operations can be (almost) completely avoided. The FPGA architecture allows us to run many independent threads with almost no latencies in memory access, thus updating up to 1024 spins per cycle. We describe Janus in detail and we summarize the physics results obtained in four years of operation of this machine; we discuss two types of physics applications: long simulations on very large systems (which try to mimic and provide understanding about the experimental non-equilibrium dynamics), and low-temperature equilibrium simulations using an artificial parallel tempering dynamics. The time scale of our non-equilibrium simulations spans eleven orders of magnitude (from picoseconds to a tenth of a second). On the other hand, our equilibrium simulations are unprecedented both because of the low temperatures reached and for the large systems that we have brought to equilibrium. A finite-time scaling ansatz emerges from the detailed comparison of the two sets of simulations. Janus has made it possible to perform spin-glass simulations that would take several decades on more conventional architectures. The paper ends with an assessment of the potential of possible future versions of the Janus architecture, based on state-of-the-art technology.

cond-mat.dis-nn↗
arXiv2012

Equilibrium fluid-solid coexistence of hard spheres

We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibb's free energies depending on several crystalline order-parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-solid interfaces). We are able to extrapolate to infinite volume the coexistence pressure (p_{co}=11.5727(10) k_B T/σ^3) and the interfacial free energy (γ_{100}=0.636(11) k_B T/σ^2).

cond-mat.stat-mech↗
arXiv2012

Thermodynamic glass transition in a spin glass without time-reversal symmetry

Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. However, spin glasses differ from structural glasses for a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behaviour of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d<6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method.

cond-mat.dis-nn↗
arXiv2011

Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic Stability and Overlap Equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda-Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks

cond-mat.dis-nn↗
arXiv2011

Comprehensive study of the critical behavior in the diluted antiferromagnet in a field

We study the critical behavior of the Diluted Antiferromagnet in a Field with the Tethered Monte Carlo formalism. We compute the critical exponents (including the elusive hyperscaling violations exponent $θ$). Our results provide a comprehensive description of the phase transition and clarify the inconsistencies between previous experimental and theoretical work. To do so, our method addresses the usual problems of numerical work (large tunneling barriers and self-averaging violations).

cond-mat.dis-nn↗
arXiv2011

The three dimensional Heisenberg spin glass under a weak random anisotropy

We perform a finite size scaling study of the three-dimensional Heisenberg spin glass in the presence of weak random anisotropic interactions, up to sizes L=32. Anisotropies have a major impact on the phase transition. The chiral-glass susceptibility does not diverge, due to a large anomalous dimension. It follows that the anisotropic spin-glass belongs to a Universality Class different from the isotropic model, which questions the applicability of the chirality scenario.

cond-mat.dis-nn↗
arXiv2011

Tethered Monte Carlo: Managing rugged free-energy landscapes with a Helmholtz-potential formalism

Tethering methods allow us to perform Monte Carlo simulations in ensembles with conserved quantities. Specifically, one couples a reservoir to the physical magnitude of interest, and studies the statistical ensemble where the total magnitude (system+reservoir) is conserved. The reservoir is actually integrated out, which leaves us with a fluctuation-dissipation formalism that allows us to recover the appropriate Helmholtz effective potential with great accuracy. These methods are demonstrating a remarkable flexibility. In fact, we illustrate two very different applications: hard spheres crystallization and the phase transition of the diluted antiferromagnet in a field (the physical realization of the random field Ising model). The tethered approach holds the promise to transform cartoon drawings of corrugated free-energy landscapes into real computations. Besides, it reduces the algorithmic dynamic slowing-down, probably because the conservation law holds non-locally.

cond-mat.stat-mech↗
arXiv2010

On the high-density expansion for Euclidean Random Matrices

Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows to group the diagrams in a small number of topological classes, providing a simple way to determine the infrared (small momenta) behavior of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.

cond-mat.dis-nn↗
arXiv2010

Static versus dynamic heterogeneities in the D = 3 Edwards-Anderson-Ising spin glass

We numerically study the aging properties of the dynamical heterogeneities in the Ising spin glass. We find that a phase transition takes place during the aging process. Statics-dynamics correspondence implies that systems of finite size in equilibrium have static heterogeneities that obey Finite-Size Scaling, thus signaling an analogous phase transition in the thermodynamical limit. We compute the critical exponents and the transition point in the equilibrium setting, and use them to show that aging in dynamic heterogeneities can be described by a Finite-Time Scaling Ansatz, with potential implications for experimental work.

cond-mat.dis-nn↗
arXiv2010

Separation and fractionation of order and disorder in highly polydisperse systems

Microcanonical Monte Carlo simulations of a polydisperse soft-spheres model for liquids and colloids have been performed for very large polydispersity, in the region where a phase-separation is known to occur when the system (or part of it) solidifies. By studying samples of different sizes, from N=256 to N=864, we focus on the nature of the two distinct coexisting phases. Measurements of crystalline order in particles of different size reveal that the solid phase segregates between a crystalline solid with cubic symmetry and a disordered phase. This phenomenon is termed fractionation.

cond-mat.soft↗
arXiv2010

Nature of the spin-glass phase at experimental length scales

We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We demonstrate the relevance of equilibrium finite-size simulations to understand experimental non-equilibrium spin glasses in the thermodynamical limit by establishing a time-length dictionary. We conclude that non-equilibrium experiments performed on a time scale of one hour can be matched with equilibrium results on L=110 lattices. A detailed investigation of the probability distribution functions of the spin and link overlap, as well as of their correlation functions, shows that Replica Symmetry Breaking is the appropriate theoretical framework for the physically relevant length scales. Besides, we improve over existing methodologies to ensure equilibration in parallel tempering simulations.

cond-mat.dis-nn↗
arXiv2010

Critical Behavior of Three-Dimensional Disordered Potts Models with Many States

We study the 3D Disordered Potts Model with p=5 and p=6. Our numerical simulations (that severely slow down for increasing p) detect a very clear spin glass phase transition. We evaluate the critical exponents and the critical value of the temperature, and we use known results at lower $p$ values to discuss how they evolve for increasing p. We do not find any sign of the presence of a transition to a ferromagnetic regime.

cond-mat.dis-nn↗
arXiv2009

Spin Glasses on the Hypercube

We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the non trivial problem of generating these lattices. Afterwards, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are: (i) the dynamics is ruled by an infinite number of time-sectors, (ii) the aging dynamics consists on the growth of coherent domains with a non vanishing surface-volume ratio, and (iii) the propagator in Fourier space follows the p^4 law. We study as well finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well.

cond-mat.dis-nn↗