arXiv subjects

A. Gordillo-Guerrero

Publications and source records attributed to A. Gordillo-Guerrero.

32 records · Page 2Linked to original sources

arXiv2011

Universal Amplitude Ratios in the Ising Model in Three Dimensions

We use a high-precision Monte Carlo simulation to determine the universal specific-heat amplitude ratio A+/A- in the three-dimensional Ising model via the impact angle ϕof complex temperature zeros. We also measure the correlation-length critical exponent νfrom finite-size scaling, and the specific-heat exponent αthrough hyperscaling. Extrapolations to the thermodynamic limit yield ϕ= 59.2(1.0) degrees, A+/A- = 0.56(3), ν= 0.63048(32) and α= 0.1086(10). These results are compatible with some previous estimates from a variety of sources and rule out recently conjectured exact values.

cond-mat.stat-mech↗

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↗

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

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↗

arXiv2010

Phase Transitions in Disordered Systems

We face the problem of phase transitions in diluted systems both from theoretical and numerical sides. We study the effects of quenched site-dilution in classical models (Heisenberg, Ising and Potts) in 2, 3, and 4 dimensions both by using the Renormalization Group and numerical simulations in the canonical and microcanonical ensembles. We propose and check a new formulation of the Finite Size Scaling ansatz (FSS) inside the microcanonical ensemble. We use microcanonical simulations to obtain a clear fist-order behavior for the diluted Potts model in 3D, estimating the tricritical dilution. We perform large-scale simulations of the 3D diluted Heisenberg model, checking its self-averaging properties. Finally we study the 4D diluted Ising model obtaining from the FSS of the specific heat a clear differentiation between the existing conflicting theories. We also compiled a large number of appendix that we expect to be used as future reference.

cond-mat.dis-nn↗

arXiv2010

The quenched-disordered Ising model in two and four dimensions

We briefly review the Ising model with uncorrelated, quenched random-site or random-bond disorder, which has been controversial in both two and four dimensions. In these dimensions, the leading exponent alpha, which characterizes the specific-heat critical behaviour, vanishes and no Harris prediction for the consequences of quenched disorder can be made. In the two-dimensional case, the controversy is between the strong universality hypothesis which maintains that the leading critical exponents are the same as in the pure case and the weak universality hypothesis, which favours dilution-dependent leading critical exponents. Here the random-site version of the model is subject to a finite-size scaling analysis, paying special attention to the implications for multiplicative logarithmic corrections. The analysis is fully supportive of the scaling relations for logarithmic corrections and of the strong scaling hypothesis in the 2D case. In the four-dimensional case unusual corrections to scaling characterize the model, and the precise nature of these corrections has been debated. Progress made in determining the correct 4D scenario is outlined.

cond-mat.stat-mech↗

arXiv2009

The Site-Diluted Ising Model in Four Dimension

In the literature, there are five distinct, fragmented sets of analytic predictions for the scaling behaviour at the phase transition in the random-site Ising model in four dimensions. Here, the scaling relations for logarithmic corrections are used to complete the scaling pictures for each set. A numerical approach is then used to confirm the leading scaling picture coming from these predictions and to discriminate between them at the level of logarithmic corrections.

cond-mat.stat-mech↗

arXiv2009

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 $ν$ 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.

cond-mat.stat-mech↗

arXiv2008

The Spin Glass Phase in the Four-State, Three-Dimensional Potts Model

We perform numerical simulations, including parallel tempering, on the Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the location of the transition and the value of the critical exponents. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the "random permutation" Potts glass.

cond-mat.dis-nn↗

arXiv2008

An in-depth view of the microscopic dynamics of Ising spin glasses at fixed temperature

Using the dedicated computer Janus, we follow the nonequilibrium dynamics of the Ising spin glass in three dimensions for eleven orders of magnitude. The use of integral estimators for the coherence and correlation lengths allows us to study dynamic heterogeneities and the presence of a replicon mode and to obtain safe bounds on the Edwards-Anderson order parameter below the critical temperature. We obtain good agreement with experimental determinations of the temperature-dependent decay exponents for the thermoremanent magnetization. This magnitude is observed to scale with the much harder to measure coherence length, a potentially useful result for experimentalists. The exponents for energy relaxation display a linear dependence on temperature and reasonable extrapolations to the critical point. We conclude examining the time growth of the coherence length, with a comparison of critical and activated dynamics.

cond-mat.dis-nn↗

arXiv2008

Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds

We study numerically the nonequilibrium dynamics of the Ising Spin Glass, for a time that spans eleven orders of magnitude, thus approaching the experimentally relevant scale (i.e. {\em seconds}). We introduce novel analysis techniques that allow to compute the coherence length in a model-independent way. Besides, we present strong evidence for a replicon correlator and for overlap equivalence. The emerging picture is compatible with non-coarsening behavior.

cond-mat.dis-nn↗

arXiv2007

First order transition in a three dimensional disordered system

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 to 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.

cond-mat.stat-mech↗

arXiv2007

Self-Averaging in the Three Dimensional Site Diluted Heisenberg Model at the critical point

We study the self-averaging properties of the three dimensional site diluted Heisenberg model. The Harris criterion \cite{critharris} states that disorder is irrelevant since the specific heat critical exponent of the pure model is negative. According with some analytical approaches \cite{harris}, this implies that the susceptibility should be self-averaging at the critical temperature ($R_χ=0$). We have checked this theoretical prediction for a large range of dilution (including strong dilution) at critically and we have found that the introduction of scaling corrections is crucial in order to obtain self-averageness in this model. Finally we have computed critical exponents and cumulants which compare very well with those of the pure model supporting the Universality predicted by the Harris criterion.

cond-mat.dis-nn↗