arXiv subjects

Marco Picco

Publications and source records attributed to Marco Picco.

At least 55 records · Page 3Linked to original sources

arXiv2014

Slicing the $3d$ Ising model: critical equilibrium and coarsening dynamics

We study the evolution of spin clusters on two dimensional slices of the $3d$ Ising model in contact with a heat bath after a sudden quench to a subcritical temperature. We analyze the evolution of some simple initial configurations, such as a sphere and a torus, of one phase embedded into the other, to confirm that their area disappears linearly in time and to establish the temperature dependence of the prefactor in each case. Two generic kinds of initial states are later used: equilibrium configurations either at infinite temperature or at the paramagnetic-ferromagnetic phase transition. We investigate the morphological domain structure of the coarsening configurations on $2d$ slices of the $3d$ system, comparing with the behavior of the bidimensional model.

cond-mat.stat-mech↗

arXiv2014

Persistence in the two dimensional ferromagnetic Ising model

We present very accurate numerical estimates of the time and size dependence of the zero-temperature local persistence in the $2d$ ferromagnetic Ising model. We show that the effective exponent decays algebraically to an asymptotic value $θ$ that depends upon the initial condition. More precisely, we find that $θ$ takes one universal value $0.199(2)$ for initial conditions with short-range spatial correlations as in a paramagnetic state, and the value $0.033(1)$ for initial conditions with the long-range spatial correlations of the critical Ising state. We checked universality by working with a square and a triangular lattice, and by imposing free and periodic boundary conditions. We found that the effective exponent suffers from stronger finite size effects in the former case.

cond-mat.stat-mech↗

arXiv2014

Diluted Antiferromagnetic 3D Ising model in a field

We present numerical simulations for the diluted antiferromagnetic 3D Ising model (DAFF) in an external magnetic field at zero temperature. Our results are compatible with the DAFF being in the same universality class as the Random Field Ising model, in agreement with the renormalization group prediction.

cond-mat.dis-nn↗

arXiv2014

A morphological study of cluster dynamics between critical points

We study the geometric properties of a system initially in equilibrium at a critical point that is suddenly quenched to another critical point and subsequently evolves towards the new equilibrium state. We focus on the bidimensional Ising model and we use numerical methods to characterize the morphological and statistical properties of spin and Fortuin-Kasteleyn clusters during the critical evolution. The analysis of the dynamics of an out of equilibrium interface is also performed. We show that the small scale properties, smaller than the target critical growing length $ξ(t) \sim t^{1/z}$ with $z$ the dynamic exponent, are characterized by equilibrium at the working critical point, while the large scale properties, larger than the critical growing length, are those of the initial critical point. These features are similar to what was found for sub-critical quenches. We argue that quenches between critical points could be amenable to a more detailed analytical description.

cond-mat.stat-mech↗

arXiv2014

On the phase transition of the 3D random field Ising model

We present numerical simulations of the random field Ising model in three dimensions at zero temperature. The critical exponents are found to agree with previous results. We study the magnetic susceptibility by applying a small magnetic field perturbation. We find that the critical amplitude ratio of the magnetic susceptibilities to be very large, equal to 233.1 \pm 1.5. We find strong sample to sample fluctuations which obey finite size scaling. The probability distribution of the size of small energy excitations is maximally non-self averaging, obeying a double peak distribution, and is finite size scaling invariant. We also study the approach to the thermodynamic limit of the ground state magnetization at the phase transition.

cond-mat.dis-nn↗

arXiv2014

How soon after a zero-temperature quench is the fate of the Ising model sealed?

We study the transient between a fully disordered initial condition and a percolating structure in the low-temperature non-conserved order parameter dynamics of the bi-dimensional Ising model. We show that a stable structure of spanning clusters establishes at a time $t_p \simeq L^{α_p}$. Our numerical results yield $α_p=0.50(2)$ for the square and kagome, $α_p=0.33(2)$ for the triangular and $α_p=0.38(5)$ for the bowtie-a lattices.We generalise the dynamic scaling hypothesis to take into account this new time-scale. We discuss the implications of these results for other non-equilibrium processes.

cond-mat.stat-mech↗

arXiv2013

Spin clusters and conformal field theory

We study numerically the fractal dimensions and the bulk three-point connectivity for the spin clusters of the Q-state Potts model in two dimensions with $1\leq Q\leq 4$. We check that the usually invoked correspondence between FK clusters and spin clusters works at the level of fractal dimensions. However, the fine structure of the conformal field theories describing critical clusters first manifests at the level of the three-point connectivities. Contrary to what recently found for FK clusters, no obvious relation emerges for generic Q between the spin cluster connectivity and the structure constants obtained from analytic continuation of the minimal model ones. The numerical results strongly suggest then that spin and FK clusters are described by conformal field theories with different realizations of the color symmetry of the Potts model.

cond-mat.stat-mech↗

arXiv2013

Connectivities of Potts Fortuin-Kasteleyn clusters and time-like Liouville correlator

Recently, two of us argued that the probability that an FK cluster in the Q-state Potts model connects three given points is related to the time-like Liouville three-point correlation function. Moreover, they predicted that the FK three-point connectivity has a prefactor which unveils the effects of a discrete symmetry, reminiscent of the S_Q permutation symmetry of the Q=2,3,4 Potts model. Their theoretical prediction has been checked for the case of percolation, corresponding to Q=1. We revisit the derivation of the time-like Liouville correlator given by Al. Zamolodchikov and show that this is the the only consistent analytic continuation of the minimal model structure constants. We then present strong numerical tests of the relation between the time-like Liouville correlator and percolative properties of the FK clusters for real values of Q.

hep-th↗

arXiv2013

Frozen into stripes: fate of the critical Ising model after a quench

In this work we study numerically the final state of the two dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at $T_c$, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing a new example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.

cond-mat.stat-mech↗

arXiv2013

Influence of long-range interactions on the critical behavior of the Ising model

We study the ferromagnetic Ising model with long-range interactions in two dimensions. We first present results of a Monte Carlo study which shows that the long-range interactions dominate over the short-range ones in the intermediate regime of interaction range. Based on a renormalization group analysis, we propose a way of computing the influence of the long-range interactions as a dimensional change.

cond-mat.stat-mech↗

arXiv2012

Critical behavior of the Ising model with long range interactions

We present results of a Monte Carlo study for the ferromagnetic Ising model with long range interactions in two dimensions. This model has been simulated for a large range of interaction parameter $σ$ and for large sizes. We observe that the results close to the change of regime from intermediate to short range do not agree with the renormalization group predictions.

cond-mat.stat-mech↗

arXiv2010

Critical interfaces and duality in the Ashkin Teller model

We report on the numerical measures on different spin interfaces and FK cluster boundaries in the Askhin-Teller (AT) model. For a general point on the AT critical line, we find that the fractal dimension of a generic spin cluster interface can take one of four different possible values. In particular we found spin interfaces whose fractal dimension is d_f=3/2 all along the critical line. Further, the fractal dimension of the boundaries of FK clusters were found to satisfy all along the AT critical line a duality relation with the fractal dimension of their outer boundaries. This result provides a clear numerical evidence that such duality, which is well known in the case of the O(n) model, exists in a extended CFT.

cond-mat.stat-mech↗

arXiv2010

Critical interfaces of the Ashkin-Teller model at the parafermionic point

We present an extensive study of interfaces defined in the Z_4 spin lattice representation of the Ashkin-Teller (AT) model. In particular, we numerically compute the fractal dimensions of boundary and bulk interfaces at the Fateev-Zamolodchikov point. This point is a special point on the self-dual critical line of the AT model and it is described in the continuum limit by the Z_4 parafermionic theory. Extending on previous analytical and numerical studies [10,12], we point out the existence of three different values of fractal dimensions which characterize different kind of interfaces. We argue that this result may be related to the classification of primary operators of the parafermionic algebra. The scenario emerging from the studies presented here is expected to unveil general aspects of geometrical objects of critical AT model, and thus of c=1 critical theories in general.

cond-mat.stat-mech↗

arXiv2009

Stark Effect of Interactive Electron-hole pairs in Spherical Semiconductor Quantum Dots

We present a theoretical variational approach, based on the effective mass approximation (EMA), to study the quantum-confinement Stark effects for spherical semiconducting quantum dots in the strong confinement regime of interactive electron-hole pair and limiting weak electric field. The respective roles of the Coulomb potential and the polarization energy are investigated in details. Under reasonable physical assumptions, analytical calculations can be performed. They clearly indicate that the Stark shift is a quadratic function of the electric field amplitude in the regime of study. The resulting numerical values are found to be in good agreement with experimental data over a significant domain of validity.

cond-mat.mes-hall↗

arXiv2009

Geometrical properties of parafermionic spin models

We present measurements of the fractal dimensions associated to the geometrical clusters for Z_4 and Z_5 spin models. We also attempted to measure similar fractal dimensions for the generalised Fortuyin Kastelyn (FK) clusters in these models but we discovered that these clusters do not percolate at the critical point of the model under consideration. These results clearly mark a difference in the behaviour of these non local objects compared to the Ising model or the 3-state Potts model which corresponds to the simplest cases of Z_N spin models with N=2 and N=3 respectively. We compare these fractal dimensions with the ones obtained for SLE interfaces.

cond-mat.stat-mech↗

arXiv2009

New Theoretical Approach to Quantum Size Effects of Interactive Electron-hole in Spherical Semiconductor Quantum Dots

The issue of quantum size effects of interactive electron-hole systems in spherical semiconductor quantum dots is put to question. A sharper theoretical approach is suggested based on a new pseudo-potential method. In this new setting, analytical computations can be performed in most intermediate steps lending stronger support to the adopted physical assumptions. The resulting numerical values for physical quantities are found to be much closer to the experimental values than those existing so far in the literature.

cond-mat.mtrl-sci↗

arXiv2008

Critical interfaces in the random-bond Potts model

We study geometrical properties of interfaces in the random-temperature q-states Potts model as an example of a conformal field theory weakly perturbed by quenched disorder. Using conformal perturbation theory in q-2 we compute the fractal dimension of Fortuin Kasteleyn domain walls. We also compute it numerically both via the Wolff cluster algorithm for q=3 and via transfer-matrix evaluations. We obtain numerical results for the fractal dimension of spin cluster interfaces for q=3. These are found numerically consistent with the duality kappa(spin) * kappa(FK)= 16 as expressed in putative SLE parameters.

cond-mat.dis-nn↗

arXiv2008

Numerical study on Schramm-Loewner Evolution in nonminimal conformal field theories

The Schramm-Loewner evolution (SLE) is a powerful tool to describe fractal interfaces in 2D critical statistical systems. Yet the application of SLE is well established for statistical systems described by quantum field theories satisfying only conformal invariance, the so called minimal conformal field theories (CFTs). We consider interfaces in Z(N) spin models at their self-dual critical point for N=4 and N=5. These lattice models are described in the continuum limit by non-minimal CFTs where the role of a Z_N symmetry, in addition to the conformal one, should be taken into account. We provide numerical results on the fractal dimension of the interfaces which are SLE candidates for non-minimal CFTs. Our results are in excellent agreement with some recent theoretical predictions.

cond-mat.other↗