A. Muñoz Sudupe

Scaling corrections: site percolation and Ising model in three dimensions

Using finite-size scaling techniques we obtain accurate results for critical quantities of the Ising model and the site percolation, in three dimensions. We pay special attention to parametrizing the corrections-to-scaling, which is necessary to bring the systematic errors below the statistical ones.

Critical exponents of the three-dimensional diluted Ising model

We study the phase diagram of the site-diluted Ising model in a wide dilution range, through Monte Carlo simulations and finite-size scaling techniques. Our results for the critical exponents and universal cumulants turn out to be dilution independent, but only after a proper infinite volume extrapolation, taking into account the leading corrections-to-scaling terms.

Finite size effects on measures of critical exponents in d = 3 O(N) models

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.

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 ≈ 0.64Tc. 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.

Nonequilibrium spin-glass dynamics from picoseconds to a tenth of a second.

We study numerically the nonequilibrium dynamics of the Ising spin glass, for a time spanning 11 orders of magnitude, thus approaching the experimentally relevant scale (i.e., seconds). We introduce novel analysis techniques to compute the coherence length in a model-independent way. We present strong evidence for a replicon correlator and for overlap equivalence. The emerging picture is compatible with noncoarsening behavior.

Critical behavior in the site-diluted three-dimensional three-state Potts model

We have studied numerically the effect of quenched site dilution on a 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

An In-Depth View of the Microscopic Dynamics of Ising Spin Glasses at Fixed Temperature

\nu

New universality class in three dimensions?: the antiferromagnetic RP2 model☆

exponent is compatible with the one of the three dimensional diluted Ising model whereas the

Measures of critical exponents in the four-dimensional site percolation

\eta

Ising exponents in the two-dimensional site-diluted Ising model

exponent is definitely different.