arXiv subjects

Victor Martin-Mayor

Publications and source records attributed to Victor Martin-Mayor.

24 records · Page 2Linked to original sources

arXiv2015

Testing statics-dynamics equivalence at the spin-glass transition in three dimensions

The statics-dynamics correspondence in spin glasses relate non-equilibrium results on large samples (the experimental realm) with equilibrium quantities computed on small systems (the typical arena for theoretical computations). Here we employ statics-dynamics equivalence to study the Ising spin-glass critical behavior in three dimensions. By means of Monte Carlo simulation, we follow the growth of the coherence length (the size of the glassy domains), on lattices too large to be thermalized. Thanks to the large coherence lengths we reach, we are able to obtain accurate results in excellent agreement with the best available equilibrium computations. To do so, we need to clarify the several physical meanings of the dynamic exponent close to the critical temperature.

cond-mat.dis-nn↗

arXiv2015

Unraveling Quantum Annealers using Classical Hardness

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, named `D-Wave' chips, promise to solve practical optimization problems potentially faster than conventional `classical' computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of quantum annealers from their classical thermal counterparts. Here, we propose a general method aimed at answering these, and apply it to experimentally study the D-Wave chip. Inspired by spin-glass theory, we generate optimization problems with a wide spectrum of `classical hardness', which we also define. By investigating the chip's response to classical hardness, we surprisingly find that the chip's performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss purely classical effects that possibly mask the quantum behavior of the chip.

quant-ph↗

arXiv2013

Universality in the three-dimensional random-field Ising model

We solve a long-standing puzzle in Statistical Mechanics of disordered systems. By performing a high-statistics simulation of the D=3 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute the complete set of critical exponents for this class, including the correction-to-scaling exponent, and we show, to high numerical accuracy, that scaling is described by two independent exponents. Discrepancies with previous works are explained in terms of strong scaling corrections.

cond-mat.dis-nn↗

arXiv2011

Ensemble equivalence in spin systems with short-range interactions

We study the problem of ensemble equivalence in spin systems with short-range interactions under the existence of a first-order phase transition. The spherical model with nonlinear nearest-neighbour interactions is solved exactly both for canonical and microcanonical ensembles. The result reveals apparent ensemble inequivalence at the first-order transition point in the sense that the microcanonical entropy is non-concave as a function of the energy and consequently the specific heat is negative. In order to resolve the paradox, we show that an unconventional saddle point should be chosen in the microcanonical calculation that represents a phase separation. The XY model with non-linear interactions is also studied by microcanonical Monte Carlo simulations in two dimensions to see how this model behaves in comparison with the spherical model.

cond-mat.stat-mech↗

arXiv2009

A cluster Monte Carlo algorithm with a conserved order parameter

We propose a cluster simulation algorithm for statistical ensembles with fixed order parameter. We use the tethered ensemble, which features Helmholtz's effective potential rather than Gibbs's free energy, and in which canonical averages are recovered with arbitrary accuracy. For the D = 2,3 Ising model our method's critical slowing down is comparable to that of canonical cluster algorithms. Yet, we can do more than merely reproduce canonical values. As an example, we obtain a competitive value for the 3D Ising anomalous dimension from the maxima of the effective potential.

cond-mat.stat-mech↗

arXiv2002

Critical structure factor in Ising systems

We perform a large-scale Monte Carlo simulation of the three-dimensional Ising model on simple cubic lattices of size L^3 with L=128 and 256. We determine the corresponding structure factor (Fourier transform of the two-point function) and compare it with several approximations and with experimental results. We also compute the turbidity as a function of the momentum of the incoming radiation, focusing in particular on the deviations from the Ornstein-Zernicke expression of Puglielli and Ford.

cond-mat.stat-mech↗