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ABSTRACT: 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 Gibbs' 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)].
Physical Review Letters 04/2012; 108(16):165701. · 7.37 Impact Factor
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ABSTRACT: We study a polydisperse soft-spheres model for colloids by means of microcanonical Monte Carlo simulations. We consider a polydispersity as high as 24%. Although solidification occurs, neither a crystal nor an amorphous state are thermodynamically stable. A finite size scaling analysis reveals that in the thermodynamic limit: (a) the fluid-solid transition is rather a crystal-amorphous phase-separation, (b) such phase-separation is preceded by the dynamic glass transition, and (c) small and big particles arrange themselves in the two phases according to a complex pattern not predicted by any fractionation scenario.
Physical Review E 08/2010; 82(2 Pt 1):021501. · 2.26 Impact Factor
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ABSTRACT: 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 figures
05/2009;
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ABSTRACT: 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.
Physical Review Letters 03/2008; 100(5):057201. · 7.37 Impact Factor
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F. Belletti,
M. Cotallo,
A Cruz,
L. A. Fernández,
A. Gordillo,
M. Guidetti,
A. Maiorano,
F. Mantovani,
E. Marinari, V. Martín-Mayor, [......],
D. Navarro,
G. Parisi,
S. Pérez-Gaviro,
M Rossi,
J. J. Ruiz-Lorenzo,
S. F. Schifano,
D. Sciretti,
A. Tarancón,
R. Tripiccione,
J. L. Velasco
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ABSTRACT: This paper describes JANUS, a modular massively parallel and reconfigurable FPGA-based computing system. Each JANUS module has a computational core and a host. The computational core is a 4x4 array of FPGA-based processing elements with nearest-neighbor data links. Processors are also directly connected to an I/O node attached to the JANUS host, a conventional PC. JANUS is tailored for, but not limited to, the requirements of a class of hard scientific applications characterized by regular code structure, unconventional data manipulation instructions and not too large data-base size. We discuss the architecture of this configurable machine, and focus on its use on Monte Carlo simulations of statistical mechanics. On this class of application JANUS achieves impressive performances: in some cases one JANUS processing element outperfoms high-end PCs by a factor ~ 1000. We also discuss the role of JANUS on other classes of scientific applications.
11/2007;
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ABSTRACT: We perform intensive numerical simulations of the three-dimensional site-diluted Ising antiferromagnet in a magnetic field at high values of the external applied field. Even if data for small lattice sizes are compatible with second-order criticality, the critical behavior of the system shows a crossover from second-order to first-order behavior for large system sizes, where signals of latent heat appear. We propose "apparent" critical exponents for the dependence of some observables with the lattice size for a generic (disordered) first-order phase transition. Comment: Final version, accepted for publication
05/2007;
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F. Belletti,
M. Cotallo,
A. Cruz,
L.A. Fernández,
A. Gordillo,
A. Maiorano,
F. Mantovani,
E. Marinari, V. Martín-Mayor,
A. Muñoz-Sudupe,
D. Navarro,
S. Pérez-Gaviro,
J.J. Ruiz-Lorenzo,
S.F. Schifano,
D. Sciretti,
A. Tarancón,
R. Tripiccione,
J.L. Velasco
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ABSTRACT: We describe the hardwired implementation of algorithms for Monte Carlo simulations of a large class of spin models. We have implemented these algorithms as VHDL codes and we have mapped them onto a dedicated processor based on a large FPGA device. The measured performance on one such processor is comparable to O(100) carefully programmed high-end PCs: it turns out to be even better for some selected spin models. We describe here codes that we are currently executing on the IANUS massively parallel FPGA-based system.
Computer Physics Communications. 04/2007;
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ABSTRACT: The phase diagram of soft spheres with size dispersion is studied by means of an optimized Monte Carlo algorithm which allows us to equilibrate below the kinetic glass transition for all size distributions. The system ubiquitously undergoes a first-order freezing transition. While for a small size dispersion the frozen phase has a crystalline structure, large density inhomogeneities appear in the highly disperse systems. Studying the interplay between the equilibrium phase diagram and the kinetic glass transition, we argue that the experimentally found terminal polydispersity of colloids is a purely kinetic phenomenon.
Physical Review Letters 03/2007; 98(8):085702. · 7.37 Impact Factor
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ABSTRACT: We show numeric evidence that, at low enough temperatures, the potential energy density of a glass-forming liquid fluctuates over length scales much larger than the interaction range. We focus on the behavior of translationally invariant quantities. The growing correlation length is unveiled by studying the finite-size effects. In the thermodynamic limit, the specific heat and the relaxation time diverge as a power law. Both features point towards the existence of a critical point in the metastable supercooled liquid phase.
Physical Review E 03/2006; 73(2 Pt 1):020501. · 2.26 Impact Factor
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ABSTRACT: We numerically study aging for the Edwards-Anderson model in three and four dimensions using different temperature-change protocols. In D=3, time scales a thousand times larger than in previous work are reached with the Spin Update Engine (SUE) machine. Deviations from cumulative aging are observed in the nonmonotonic time behavior of the coherence length. Memory and rejuvenation effects are found in a temperature-cycle protocol, revealed by vanishing effective waiting times. Similar effects are reported for the D=3 site-diluted ferromagnetic Ising model (without chaos). However, rejuvenation is reduced if off-equilibrium corrections to the fluctuation-dissipation theorem are considered. Memory and rejuvenation are quantitatively describable in terms of the growth regime of the spin-glass coherence length.
Phys. Rev. B. 08/2005; 72(5).
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ABSTRACT: The spin update engine (SUE) machine is used to extend, by a factor of 1000, the timescale of previous studies of the ageing, out-of-equilibrium dynamics of the Edwards–Anderson model with binary couplings, on large lattices (L = 60). The correlation function, C(t + tw, tw), tw being the time elapsed under a quench from high-temperature, follows nicely a slightly-modified power law for t > tw. Very small (logarithmic), yet clearly detectable deviations from the full-ageing t/tw scaling can be observed. Furthermore, the t < tw data show clear indications of the presence of more than one time sector in the ageing dynamics. Similar results are found in four dimensions, but a rather different behaviour is obtained in the infinite-dimensional z = 6 Viana–Bray model. Most surprisingly, our results in infinite dimensions seem incompatible with dynamical ultrametricity. A detailed study of the link correlation function is presented, suggesting that its ageing properties are the same as for the spin correlation function.
Journal of Physics A General Physics 10/2003; 36(43):10755.
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ABSTRACT: Glasses are amorphous solids, in the sense that they display elastic behaviour. In crystalline solids, elasticity is associated with phonons, which are quantized vibrational excitations. Phonon-like excitations also exist in glasses at very high (terahertz; 10(12) Hz) frequencies; surprisingly, these persist in the supercooled liquids. A universal feature of such amorphous systems is the boson peak: the vibrational density of states has an excess compared to the Debye squared-frequency law. Here we investigate the origin of this feature by studying the spectra of inherent structures (local minima of the potential energy) in a realistic glass model. We claim that the 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 boson peak moves to lower frequencies on approaching the phonon-saddle transition, and its height diverges at the critical point. Our numerical results agree with the predictions of euclidean random matrix theory on the existence of a sharp phase transition between an amorphous elastic phase and a phonon-free one.
Nature 04/2003; 422(6929):289-92. · 36.28 Impact Factor
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ABSTRACT: Considering the disorder caused in manganites by the substitution Mn→Fe or Ga, we accomplish a systematic study of doped manganites begun in previous papers. To this end, a disordered model is formulated and solved using the variational mean-field technique. The subtle interplay between double exchange, superexchange, and disorder causes similar effects on the dependence of TC on the percentage of Mn substitution in the cases considered. Yet, in La2/3Ca1/3Mn1-yGayO3 our results suggest a quantum critical point (QCP) for y≈0.1–0.2, associated to the localization of the electronic states of the conduction band. In the case of LaxCaxMn1-yFeyO3 (with x=1/3,3/8) no such QCP is expected.
Phys. Rev. B. 09/2002; 66(10).
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ABSTRACT: The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the particles oscillate around randomly distributed centers, interacting through a generic pair potential. We present results of a resummation of the perturbative expansion in the inverse particle density for the dynamic structure factor and density of states. This gives accurate results for the range of densities found in real systems.
Physical Review Letters 09/2001; 87(8):085502. · 7.37 Impact Factor
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ABSTRACT: We study the phase diagram of the double exchange model, with antiferromagnetic interactions, in a cubic lattice both at zero and at finite temperature. There is a rich variety of magnetic phases, combined with regions where phase separation takes place. We identify phases, intrinsic to the cubic lattice, which are stable for realistic values of the interactions and dopings. Some of these phases break chiral symmetry, leading to unusual features. Comment: 8 pages, 6 postscript figures
Physical Review B 07/2001; 64(054408). · 3.69 Impact Factor
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ABSTRACT: We study the temperature-dilution phase diagram of a site-diluted Heisenberg antiferromagnet on a fcc lattice, with and without the Dzyaloshinskii-Moriya anisotropic term, fixed to realistic microscopic parameters for $IIB_{1-x} Mn_x Te$ (IIB=Cd, Hg, Zn). We show that the dipolar Dzyaloshinskii-Moriya anisotropy induces a finite-temperature phase transition to a spin glass phase, at dilutions larger than 80%. The resulting probability distribution of the order parameter P(q) is similar to the one found in the cubic lattice Edwards-Anderson Ising model. The critical exponents undergo large finite size corrections, but tend to values similar to the ones of the Edwards-Anderson-Ising model. Comment: 4 pages plus 3 postscript figures
02/2000;
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ABSTRACT: We have studied numerically the effect of quenched site dilution on a
weak 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 ν
exponent is compatible with the one of the three-dimensional diluted
Ising model, whereas the η exponent is definitely different.
Physical review. B, Condensed matter 01/2000; 61:3215-3218.
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ABSTRACT: We study the spectral width as a function of the external momentum for the dynamical structure factor of a disordered harmonic solid, considered as a toy model for supercooled liquids and glasses. Both in the context of single-link coherent potential approximation and of a single-defect approximation, two different regimes are clearly identified: if the density of states at zero energy is zero, the Rayleigh $p^4$ law is recovered for small momentum. On the contrary, if the disorder induces a non vanishing density of states at zero energy, a linear behaviour is obtained. The dynamical structure factor is numerically calculated in lattices as large as $96^3$, and satisfactorily agrees with the analytical computations. Comment: 7 pages plus 4 postscript figures
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 11/1999;
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ABSTRACT: 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.
Nuclear Physics B. 07/1997;
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ABSTRACT: We study the critical properties of three-dimensional O(N) models, for N = 2, 3, 4. Parameterizing the leading corrections-to-scaling for the η exponent, we obtain a reliable infinite volume extrapolation, incompatible with previous Monte Carlo values, but in agreement with ϵ-expansions. We also measure the critical exponent related with the tensorial magnetization as well as the ν exponents and critical couplings.
Physics Letters B. 06/1996;
