arXiv subjects

C. L. Ullod

Publications and source records attributed to C. L. Ullod.

10 recordsLinked to original sources

arXiv2000

Critical Behavior of the Three-Dimensional Ising Spin Glass

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.

cond-mat.dis-nn↗

arXiv2000

SUE: A Special Purpose Computer for Spin Glass Models

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.

cond-mat.dis-nn↗

arXiv1999

Study of a microcanonical algorithm on the $\pm J$ spin glass model in d=3

We consider a microcanonical local algorithm to be applied on the $\pm J$ spin glass model. We have compared the results coming from a microcanonical Monte Carlo simulation with those from a canonical one: Thermalization times, spin glass susceptibilities and Binder parameters. For a fixed lattice size we found different results between the two thermodynamic ensembles, which tend to vanish at bigger volumes. Moreover, microcanonical thermalization times are longer than the canonical ones. Finally we have checked that one of the Guerra relations is satisfied with good precision for the two largest lattices.

cond-mat.dis-nn↗

arXiv1999

Inverse Symmetry Breaking on the lattice: an accurate MC study

We present here a new MC study of ISB at finite temperature in a $Z_2\times Z_2$ $λϕ^4$ model in four dimensions. The results of our simulations, even if not conclusive, are favourable to ISB. Detection of the effect required measuring some critical couplings with six-digits precision, a level of accuracy that could be achieved only by a careful use of FSS techniques. The gap equations for the Debye masses, resulting from the resummation of the ring diagrams, seem to provide a qualitatively correct description of the data, while the simple one-loop formulae appear to be inadequate.

hep-lat↗

arXiv1998

A Monte Carlo study of Inverse Symmetry Breaking

We make a Monte Carlo study of the coupled two-scalar $λϕ^2_1ϕ^2_2$ model in four dimensions at finite temperature. We find no trace of Inverse Symmetry Breaking for values of the renormalized parameters for which perturbation theory predicts this phenomenon.

hep-lat↗

arXiv1998

A lattice Monte Carlo study of Inverse Symmetry Breaking in a two-scalar model in three dimensions

We carry a Monte Carlo study of the coupled two-scalar $λϕ^2_1 ϕ^2_2$ model in three dimensions. We find no trace of Inverse Symmetry Breaking in the region of negative $λ$'s for which the one-loop effective potential predicts this phenomenon. Moreover, for $λ$'s negative enough, but still in the stability region for the potential, one of the transitions turns out to be of first order, both for zero and finite temperature.

hep-lat↗

arXiv1996

A Dedicated Computer for Ising-like Spin Glass Models

We present a parallel machine, based on programmable devices, dedicated to simulate spin glass models with Z2 variables and short range interaction. A working prototype is described for two lattices containing 312x312 spins each with an update time of 50 ns per spin. The final version of the three dimensional parallel machine is discussed with spin update time up to 312 ps.

hep-lat↗

arXiv1996

Continuum limit of finite temperature $λϕ^4_3$ from lattice Monte Carlo

The $ϕ^4_3$ model at finite temperature is simulated on the lattice. For fixed $N_t$ we compute the transition line for $N_s \to \infty$ by means of Finite Size Scaling techniques. The crossings of a Renormalization Group trajectory with the transition lines of increasing $N_t$ give a well defined limit for the critical temperature in the continuum. By considering different RG trajectories, we compute $T^c/g$ as a function of the renormalized parameters.

hep-lat↗

arXiv1996

Antiferromagnetism in four dimensions: search for non-triviality

We present antiferromagnetism as a mechanism capable of modifying substantially the phase diagram and the critical behaviour of statistical mechanical models. This is particularly relevant in four dimensions, due to the connection between second order transition points and the continuum limit as a quantum field theory. We study three models with an antiferromagnetic interaction: the Ising and the O(4) Models with a second neighbour negative coupling, and the $\RP{2}$ Model. Different conclusions are obtained depending on the model.

hep-lat↗

arXiv1996

Phase diagram of d=4 Ising Model with two couplings

We study the phase diagram of the four dimensional Ising model with first and second neighbour couplings, specially in the antiferromagnetic region, by using Mean Field and Monte Carlo methods. From the later, all the transition lines seem to be first order except that between ferromagnetic and disordered phases in a region including the first-neighbour Ising transition point.

hep-lat↗