arXiv subjects
Publications and source records attributed to A. Cruz.
We study the fluctuation-dissipation relations for a three dimensional Ising spin glass in a magnetic field both in the high temperature phase as well as in the low temperature one. In the region of times simulated we have found that our results support a picture of the low temperature phase with broken replica symmetry, but a droplet behavior can not be completely excluded.
It is shown that a bosonic formulation of the double-exchange model, one of the classical models for magnetism, generates dynamically a gauge-invariant phase in a finite region of the phase diagram. We use analytical methods, Monte Carlo simulations and Finite-Size Scaling analysis. We study the transition line between that region and the paramagnetic phase. The numerical results show that this transition line belongs to the Universality Class of the Antiferromagnetic RP(2) model. The fact that one can define a Universality Class for the Antiferromagnetic RP(2) model, different from the one of the O(N) models, is puzzling and somehow contradicts naive expectations about Universality.
We have simulated, using parallel tempering, the three dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L=20) has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, a strong evidence for a second-order finite temperature phase transition ruling out other possible scenarios like a Kosterlitz-Thouless phase transition. Precise values for the $ν$ and $η$ critical exponents are also presented.
The use of last generation Programmable Electronic Components makes possible the construction of very powerful and competitive special purpose computers. We have designed, constructed and tested a three-dimensional Spin Glass model dedicated machine, which consists of 12 identical boards. Each single board can simulate 8 different systems, updating all the systems at every clock cycle. The update speed of the whole machine is 217ps/spin with 48 MHz clock frequency. A device devoted to fast random number generation has been developed and included in every board. The on-board reprogrammability permits us to change easily the lattice size, or even the update algorithm or the action. We present here a detailed description of the machine and the first runs using the Heat Bath algorithm.
We study the pure compact U(1) gauge theory with the extended Wilson action (β, γcouplings) by finite size scaling techniques, in lattices ranging from L=6 to L=24 in the region of γ<= 0 with toroidal and spherical topologies. The phase transition presents a double peak structure which survives in the thermodynamical limit in the torus. In the sphere the evidence support the idea of a weaker, but still first order, phase transition. For negative values of gamma the transition becomes weaker and larger lattices are needed to find its asymptotic behaviour. Along the transient region the behaviour is the typical one of a weak first order transition for both topologies, with a region where 1/d < nu < 0.5, which becomes nu compatible with 1/d when larger lattices are used.
The order of the Coulomb-Higgs transition in the U(1)-Higgs model with unfrozen modulus of the scalar field is studied. Large lattices (up to $24^4$ in one case) and high statistics are used. We fix $β=1.15$ and explore specially a region of $λ$-values where metastability is observed. We study the thermodynamical limit of several observables, in particular, the latent heat, the specific heat, the decrement of the free energy between the maxima and the central minimum of the two-peaked histogram, the Binder cumulant and the displacement of the critical coupling with the lattice size. The results point towards a second order transition for $λ\gtrsim 0.005$, while for smaller values of $λ$ the strong metastability growing with the lattice size seems to derive from a first order character.
We have made a study of several update algorithms using the XY model. We find that sequential local overrelaxation is not ergodic at the scale of typical Monte Carlo simulation time. We have introduced a new multisite microcanonical update method, which yields results compatible with those of random overrelaxation and the microcanonical demon algorithm, which are very much slower, all being incompatible with the sequential overrelaxation results.
We find a first order Coulomb--Higgs phase transition at moderately large values of the coupling $λ$, and no evidence for a change of order at any finite value of it.