arXiv subjects

Ricardo Paredes

Publications and source records attributed to Ricardo Paredes.

7 recordsLinked to original sources

arXiv2009

On the critical behavior of two-dimensional liquid crystals

The Lebwohl-Lasher (LL) model is the traditional model used to describe the nematic-isotropic transition of real liquid crystals. In this paper, we develop a numerical study of the temperature behaviour and of finite-size scaling of the two-dimensional (2D) LL-model. We discuss two possible scenarios. In the first one, the 2D LL-model presents a phase transition similar to the topological transition appearing in the 2D XY-model. In the second one, the 2D LL-model does not exhibit any critical transition, but its low temperature behaviour is rather characterized by a crossover from a disordered phase to an ordered phase at zero temperature. We realize and discuss various comparisons with the 2D XY-model and the 2D Heisenberg model. Adding to previous studies of finite-size scaling behaviour of the order parameter and conformal mapping of order parameter profile, we analyze the critical scaling of the probability distribution function, hyperscaling relations and stiffness order parameter and conclude that the second scenario (no critical transition) is the most plausible.

cond-mat.stat-mech↗

arXiv2008

Identification and characterization of icosahedral metallic nanowires

We present and discuss an algorithm to identify and characterize the long icosahedral structures (staggered pentagonal nanowires with 1-5-1-5 atomic structure) that appear in Molecular Dynamics simulations of metallic nanowires of different species subjected to stretching. The use of the algorithm allows the identification of pentagonal rings forming the icosahedral structure as well as the determination of its number, and the maximum length of the pentagonal nanowire. The algorithm is tested with some ideal structures to show its ability to discriminate between pentagonal rings and other ring structures. We applied the algorithm to Ni nanowires with temperatures ranging between 4K and 865K, stretched along the [100] direction. We studied statistically the formation of pentagonal nanowires obtaining the distributions of the maximum length and number of rings as function of the temperature. The pentagonal nanowire maximum length distribution presents a peaked shape, with peaks locate at fixes distances whose separa-tion corresponds to the distance between two consecutive pentagonal rings.

cond-mat.mtrl-sci↗

arXiv2008

No quasi-long-range order in the two-dimensional liquid crystal

Systems with global symmetry group O(2) experience topological transition in the 2-dimensional space. But there is controversy about such a transition for systems with global symmetry group O(3). In this paper, we study the Lebwohl-Lasher model for the two-dimensional liquid crystal, using three different methods independent of the proper values of possible critical exponents. Namely, we analyze the at-equilibrium order parameter distribution function with: 1) the hyperscaling relation; 2) the first scaling collapse for the probability distribution function;and 3) the Binder's cumulant. We give strong evidences for definite lack of a line of critical points at low temperatures in the Lebwohl-Lasher model, contrary to conclusions of a number of previous numerical studies.

cond-mat.stat-mech↗

arXiv2006

Effects of aerogel-like disorder on the critical behavior of O(m)-vector models. Recent simulations and experimental evidences

We review some results on the effect of a specific type of quenched disorder on well known O(m)-vector models in three dimension. Evidences of changes of criticality in both systems, when confined in aerogel pores, are briefly referenced. The 3DXY model (m=2) represents the universality class to which the λ-transition of bulk superfluid $^4$He belongs. Experiments report changes of critical exponents for this transition, when superfluid $^4$He is confined in aerogels. Numerical results of the 3DXY model, confined in aerogel-like structures, are in agreement with experiments. Both results seem to contradict Harris criterion: being the specific heat exponent negative for the pure system, changes must be explained in terms of the extended criterion due to Weinrib and Halperin, which requires disorder to be long-range correlated (LRC) at all scales. Aerogels are fractal through some decades only, and present crossovers to homogeneous regimes at finite scales, so the violation to Harris criterion persists. The apparent violation has been explained in terms of hidden LRC subsets within aerogels $[$Phys. Rev. Lett., 2003, {\bf 90}, 170602$]$. On the other hand, experiments on the liquid-vapor (LV) transition of $^4$He and N$_2$ confined in aerogels, also showed changes in critical-point exponents. Being the LV critical-point in the O(1) universality class, criticality may be affected by both, short-range correlated (SRC) and LRC subsets ofdisorder. Simulations of the 3DIS in DLCA aerogels can corroborate experimental results. Experiments and simulations both suggest a shift in critical exponents to values closer to the SRC instead of those of the LRC fixed point.

cond-mat.dis-nn↗

arXiv2006

Three-dimensional Ising model confined in low-porosity aerogels: a Monte Carlo study

The influence of correlated impurities on the critical behaviour of the 3D Ising model is studied using Monte Carlo simulations. Spins are confined into the pores of simulated aerogels (diffusion limited cluster-cluster aggregation) in order to study the effect of quenched disorder on the critical behaviour of this magnetic system. Finite size scaling is used to estimate critical couplings and exponents. Long-range correlated disorder does not affect critical behavior. Asymptotic exponents differ from those of the pure 3D Ising model (3DIS), but it is impossible, with our precision, to distinguish them from the randomly diluted Ising model (RDIS).

cond-mat.stat-mech↗

arXiv2005

Nematic phase transitions in two-dimensional systems

Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The system is studied through standard Finite-Size Scaling and conformal rescaling of density profiles or correlation functions. The low temperature limit is discussed in the spin wave approximation and confirms the numerical results, while the value of the correlation function exponent at the deconfining transition seems controversial.

cond-mat.stat-mech↗

arXiv2005

Topological transition in a two-dimensional model of liquid crystal

Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The system is studied through standard Finite-Size Scaling and conformal rescaling of density profiles of correlation functions. A topological transition between a paramagnetic phase at high temperature and a critical phase at low temperature is observed. The low temperature limit is discussed in the spin wave approximation and confirms the numerical results.

cond-mat.stat-mech↗