arXiv subjects

A. Coniglio

Publications and source records attributed to A. Coniglio.

44 records · Page 3Linked to original sources

arXiv1998

Cluster formulation of spin glasses and the frustrated percolation model: statics and dynamics

We study the properties of the q-state frustrated bond percolation model by a Monte Carlo "bond flip" dynamics, using an algorithm originally devised by Sweeny and suitably modified to treat the presence of frustration. We analyze the percolation transition of the model, and find that it falls in the universality class of the q/2-state ferromagnetic Potts model. We then investigate the bond flip dynamics of the model, and find that for temperatures lower than the percolation transition Tp the relaxation functions show a two step decay, reminiscent of the relaxation of glass forming liquids. The long time decay (alpha-relaxation) is well fitted for T<Tp by a stretched exponential function, showing that in this model the relevant mechanism for the appearing of stretched exponentials is the percolation transition. At very low temperatures the relaxation functions develop a long plateau, as observed in glass forming liquids.

cond-mat.stat-mech↗

arXiv1998

Percolation transition and the onset of non exponential relaxation in fully frustrated models

We numerically study the dynamical properties of fully frustrated models in 2 and 3 dimensions. The results obtained support the hypothesis that the percolation transition of the Kasteleyn-Fortuin clusters corresponds to the onset of stretched exponential autocorrelation functions in systems without disorder. This dynamical behavior may be due to the ``large scale'' effects of frustration, present below the percolation threshold. Moreover these results are consistent with the picture suggested by Campbell et al. in space of configurations.

cond-mat.stat-mech↗

arXiv1998

The Mean Field Theory for Percolation Models of the Ising Type

The $q=2$ random cluster model is studied in the context of two mean field models: The Bethe lattice and the complete graph. For these systems, the critical exponents that are defined in terms of finite clusters have some anomalous values as the critical point is approached from the high density side which vindicates the results of earlier studies. In particular, the exponent $\tilde γ^\prime$ which characterises the divergence of the average size of finite clusters is 1/2 and $\tildeν^\prime$, the exponent associated with the length scale of finite clusters is 1/4. The full collection of exponents indicates an upper critical dimension of 6. The standard mean field exponents of the Ising system are also present in this model ($ν^\prime = 1/2$, $γ^\prime = 1$) which implies, in particular, the presence of two diverging length scales. Furthermore, the finite cluster exponents are stable to the addition of disorder which, near the upper critical dimension, may have interesting implications concerning the generality of the disordered system/correlation length bounds.

cond-mat.stat-mech↗

arXiv1997

Glassy behavior of the site frustrated percolation model

The dynamical properties of the site frustrated percolation model are investigated and compared with those of glass forming liquids. When the density of the particles on the lattice becomes high enough, the dynamics of the model becomes very slow, due to geometrical constraints, and rearrangement on large scales is needed to allow relaxation. The autocorrelation functions, the specific volume for different cooling rates, and the mean square displacement are evaluated, and are found to exhibit glassy behavior.

cond-mat.stat-mech↗

arXiv1997

Non exponential relaxation in fully frustrated models

We study the dynamical properties of the fully frustrated Ising model. Due to the absence of disorder the model, contrary to spin glass, does not exhibit any Griffiths phase, which has been associated to non-exponential relaxation dynamics. Nevertheless we find numerically that the model exhibits a stretched exponential behavior below a temperature T_p corresponding to the percolation transition of the Kasteleyn-Fortuin clusters. We have also found that the critical behavior of this clusters for a fully frustrated q-state spin model at the percolation threshold is strongly affected by frustration. In fact while in absence of frustration the q=1 limit gives random percolation, in presence of frustration the critical behavior is in the same universality class of the ferromagnetic q=1/2-state Potts model.

cond-mat.stat-mech↗

arXiv1997

Invaded Cluster Dynamics for Frustrated Models

The Invaded Cluster (IC) dynamics introduced by Machta et al. [Phys. Rev. Lett. 75 2792 (1995)] is extended to the fully frustrated Ising model on a square lattice. The properties of the dynamics which exhibits numerical evidence of self-organized criticality are studied. The fluctuations in the IC dynamics are shown to be intrinsic of the algorithm and the fluctuation-dissipation theorem is no more valid. The relaxation time is found very short and does not present critical size dependence.

cond-mat.stat-mech↗

arXiv1996

Percolation and cluster Monte Carlo dynamics for spin models

A general scheme for devising efficient cluster dynamics proposed in a previous letter [Phys.Rev.Lett. 72, 1541 (1994)] is extensively discussed. In particular the strong connection among equilibrium properties of clusters and dynamic properties as the correlation time for magnetization is emphasized. The general scheme is applied to a number of frustrated spin model and the results discussed.

cond-mat↗

arXiv1995

Early stage scaling in phase ordering kinetics

A global analysis of the scaling behaviour of a system with a scalar order parameter quenched to zero temperature is obtained by numerical simulation of the Ginzburg-Landau equation with conserved and non conserved order parameter. A rich structure emerges, characterized by early and asymptotic scaling regimes, separated by a crossover. The interplay among different dynamical behaviours is investigated by varying the parameters of the quench and can be interpreted as due to the competition of different dynamical fixed points.

cond-mat↗