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D Espriu

Publications and source records attributed to D Espriu.

4 recordsLinked to original sources
PubMed2004

Dynamics of the two-dimensional gonihedric spin model.

In this paper, we study dynamical aspects of the two-dimensional (2D) gonihedric spin model using both numerical and analytical methods. This spin model has vanishing microscopic surface tension and it actually describes an ensemble of loops living on a 2D surface. The self-avoidance of loops is parametrized by a parameter kappa . The kappa=0 model can be mapped to one of the six-vertex models discussed by Baxter, and it does not have critical behavior. We have found that allowing for kappa not equal 0 does not lead to critical behavior either. Finite-size effects are rather severe, and in order to understand these effects, a finite-volume calculation for non-self-avoiding loops is presented. This model, like his 3D counterpart, exhibits very slow dynamics, but a careful analysis of dynamical observables reveals nonglassy evolution (unlike its 3D counterpart). We find, also in this kappa=0 case, the law that governs the long-time, low-temperature evolution of the system, through a dual description in terms of defects. A power, rather than logarithmic, law for the approach to equilibrium has been found.

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PubMed2002

Slow dynamics in the three-dimensional gonihedric model.

We study dynamical aspects of three-dimensional gonihedric spins by using Monte-Carlo methods. These models have a purely geometrical motivation, deriving from string and random surface theory. Here, however, we shall analyze this family of models just from a statistical point of view. In particular, we shall be concerned with their ability to exhibit remarkably slow dynamics and seemingly glassy behavior below a certain temperature T(g), without the need of introducing disorder of any kind. We consider first a Hamiltonian that takes into account only a four-spin term (kappa=0), where a first-order phase transition is well established. By studying the relaxation properties at low temperatures, we confirm that the model exhibits two distinct regimes. For T(g)<T<T(c), with long lived metastability and a supercooled phase, the approach to equilibrium is well described by a stretched exponential. For T<T(g), the dynamics appears to be logarithmic. We provide an accurate determination of T(g). We also determine the evolution of particularly long lived configurations. Next, we consider the case kappa=1, where the plaquette term is absent and the gonihedric action consists in a ferromagnetic Ising with fine-tuned next-to-nearest neighbor interactions. This model exhibits a second order phase transition. The consideration of the relaxation time for configurations in the cold phase reveals the presence of slow dynamics and glassy behavior for any T<T(c). Type-II aging features are exhibited by this model.

Journal Article↗
PubMed2000

Slow dynamics of ising models with energy barriers

Using Monte Carlo simulations we study the dynamics of three-dimensional Ising models with nearest-, next-nearest-, and four-spin (plaquette) interactions. During coarsening, such models develop growing energy barriers, which leads to very slow dynamics at low temperature. As already reported, the model with only the plaquette interaction exhibits some of the features characteristic of ordinary glasses: strong metastability of the supercooled liquid, a weak increase of the characteristic length under cooling, stretched-exponential relaxation, and aging. The addition of two-spin interactions, in general, destroys such behavior: the liquid phase loses metastability and the slow-dynamics regime terminates well below the melting transition, which is presumably related with a certain corner-rounding transition. However, for a particular choice of interaction constants, when the ground state is strongly degenerate, our simulations suggest that the slow-dynamics regime extends up to the melting transition. The analysis of these models leads us to the conjecture that in the four-spin Ising model domain walls lose their tension at the glassy transition and that they are basically tensionless in the glassy phase.

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