Person: Martín Mayor, Víctor
Universidad Complutense de Madrid
Faculty / Institute
Now showing 1 - 10 of 136
- PublicationPhase diagram and quasiparticles of a lattice SU(2) scalar-fermion model in 2+1 dimensions(Amer Physical Soc, 2000-02-01) Alonso, J.L.; Boucaud, Ph.; Martín Mayor, Víctor; van der Sijs, A.J.The phase diagram at zero temperature of a lattice SU(2) scalar-fermion model in 211 dimensions is studied numerically and with mean-field methods. Special attention is devoted to the strong coupling regime. We have developed a new method to adapt the hybrid Monte Carlo algorithm to the O(3) non-linear σ model constraint. The charged excitations in the various phases are studied at the mean-field level. Bound states of two charged fermions are found in a strongly coupled paramagnetic phase. On the other hand, in the strongly coupled antiferromagnetic phase fermionic excitations around momenta (±π/2, ±π/2, ±π/2) emerge.
- PublicationNumerical construction of the Aizenman-Wehr metastate(American Physical Society, 2017-07-21) Billoire,, A.; Fernández Pérez, Luis Antonio; Maiorano, A.; Marinari, E.; Martín Mayor, Víctor; Moreno Gordo, J.; Parisi, G.; Ricci-Tersenghi, F.; Ruiz Lorenzo, J. J.Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. We present a numerical construction of the metastate for the d ¼ 3 Ising spin glass. We work in equilibrium, below the critical temperature. Leveraging recent rigorous results, our numerical analysis gives evidence for a dispersed metastate, supported on many thermodynamic states.
- PublicationThe four-dimensional site-diluted Ising model: A finite-size scaling study(Elsevier, 1998-02-23) Ballesteros, H. G.; Fernández Pérez, Luis Antonio; Martín Mayor, Víctor; Muñoz Sudupe, Antonio; Parisi, G.; Ruiz Lorenzo, J. J.Using finite-size scaling techniques, we study the critical properties of the site-diluted Ising model in four dimensions. We carry out a high-statistics Monte Carlo simulation for several values of the dilution. The results support the perturbative scenario: there is only the Ising fixed point with large logarithmic scaling corrections. We obtain, using the Perturbative Renormalization Group, functional forms for the scaling of several observables that are in agreement with the numerical data.
- PublicationJanus II: A new generation application-driven computer for spin-system simulations(Elsevier Science Ltd, 2014-02) Baity Jesi, Marco; Fernández Pérez, Luis Antonio; Martín Mayor, Víctor; Muñoz Sudupe, Antonio; Otros, ...This paper describes the architecture, the development and the implementation of Janus II, a new generation application-driven number cruncher optimized for Monte Carlo simulations of spin systems (mainly spin glasses). This domain of computational physics is a recognized grand challenge of high-performance computing: the resources necessary to study in detail theoretical models that can make contact with experimental data are by far beyond those available using commodity computer systems. On the other hand, several specific features of the associated algorithms suggest that unconventional computer architectures – that can be implemented with available electronics technologies – may lead to order of magnitude increases in performance, reducing to acceptable values on human scales the time needed to carry out simulation campaigns that would take centuries on commercially available machines. Janus II is one such machine, recently developed and commissioned, that builds upon and improves on the successful JANUS machine, which has been used for physics since 2008 and is still in operation today. This paper describes in detail the motivations behind the project, the computational requirements, the architecture and the implementation of this new machine and compares its expected performances with those of currently available commercial systems.
- PublicationMean-value identities as an opportunity for Monte Carlo error reduction(American Physical Society, 2009-05-11) Fernández Pérez, Luis Antonio; Martín Mayor, VíctorIn the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.
- PublicationThe Boson peak and the phonons in glasses(American Institute of Physics, 2004-06) Ciliberti, S.; Grigera, T.S.; Martín Mayor, Víctor; Parisi, G.; Verrocchio, P.Despite the presence of topological disorder, phonons seem to exist also in glasses at very high frequencies (THz) and they remarkably persist into the supercooled liquid. A universal feature of such a systems is the Boson peak, an excess of states over the standard Debye contribution at the vibrational density of states. Exploiting the euclidean random matrix theory of vibrations in amorphous systems, we show that this peak is the signature of a phase transition in the space of the stationary points of the energy, from a minima-dominated phase (with phonons) at low energy to a saddle-point dominated phase (without phonons). The theoretical predictions are checked by means of numeric simulations.
- PublicationFirst-order transition in a three-dimensional disordered system(American Physical Society, 2008-02-08) Fernández Pérez, Luis Antonio; Gordillo Guerrero, A.; Martín Mayor, Víctor; Ruiz Lorenzo, J. J.We present the first detailed numerical study in three dimensions of a first-order phase transition that remains first order in the presence of quenched disorder (specifically, the ferromagnetic-paramagnetic transition of the site-diluted four states Potts model). A tricritical point, which lies surprisingly near the pure-system limit and is studied by means of finite-size scaling, separates the first-order and second-order parts of the critical line. This investigation has been made possible by a new definition of the disorder average that avoids the diverging-variance probability distributions that plague the standard approach. Entropy, rather than free energy, is the basic object in this approach that exploits a recently introduced microcanonical Monte Carlo method.
- PublicationSummability of the perturbative expansion for a zero-dimensional disordered spin model(IOP Publishing, 2000-02-11) Álvarez, Gabriel; Martín Mayor, Víctor; Ruiz Lorenzo, Juan J.We show analytically that the perturbative expansion for the free energy of the zero dimensional (quenched) disordered Ising model is Borel-summable in a certain range of parameters, provided that the summation is carried out in two steps: first, in the strength of the original coupling of the Ising model and subsequently in the variance of the quenched disorder. This result is illustrated by some high-precision calculations of the free energy obtained by a straightforward numerical implementation of our sequential summation method.
- PublicationReconfigurable computing for Monte Carlo simulations: results and prospects of the Janus project(Springer Heidelberg, 2012-08) Baity Jesi, Marco; Fernández Pérez, Luis Antonio; Martín Mayor, Víctor; Muñoz Sudupe, Antonio; otros, ...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.
- PublicationIon kinetic transport in TJ-II(American Institute of Physics, 2008) Velasco, J. L.; Castejón, F.; Fernández Pérez, Luis Antonio; Martín Mayor, Víctor; Tarancón, A.The ion Drift Kinetic Equation (DKE) which describes the ion coUisional transport is solved for the TJ-II device plasmas. This non-linear equation is computed by peribrming a mean field iterative calculation. In each step of the calculation, a Fokker-Planck equation is solved by means of the Langevin approach: one million particles are followed in a realistic TJ-II magnetic configuration, taking into account collisions and electric field. This allows to avoid the assumptions made in the usual neoclassical approach, namely considering radially narrow particle trajectories, diffusive transport, energy conservation and infinite parallel transport. As a consequence, global features of transport, not present in the customary neoclassical models, appear: non-diffusive transport and asymmetries on the magnetic surfaces.