arXiv subjects

Tiago J. Oliveira

Publications and source records attributed to Tiago J. Oliveira.

30 records · Page 2Linked to original sources

arXiv2019

Order-disorder transition in a two-dimensional associating lattice gas

We study an associating lattice gas (ALG) using Monte Carlo simulation and solutions on Husimi lattices. In this model, the molecules have an orientational degree of freedom and the interactions depend on the relative orientations of nearest-neighbor molecules. We focus on the transition between the high-density liquid (HDL) phase and the isotropic gas phase in the limit of full occupancy ($μ\to \infty$). Simulation results show a continuous phase transition at $τ_c=k_BT_c/γ=0.4763(1)$ (where $-γ$ is the bond energy) between the low-temperature HDL phase, with a non-vanishing mean orientation of the molecules, and the high-temperature isotropic phase. Results for critical exponents and the Binder cumulant indicate that the transition belongs to the three-state Potts model universality class, even though the ALG Hamiltonian does not have the full permutation symmetry of the Potts model. In contrast with simulation, the Husimi lattice results furnish a discontinuous phase transition, characterized by a discontinuity of the nematic order parameter. The transition temperatures ($τ_c=0.51403$ and $0.51207$ for trees built with triangles and hexagons, respectively) are slightly higher than the one found via simulation. Since the Husimi lattice studies show that the ALG phase diagram features a discontinuous gas-HDL line for finite $μ$, three possible scenarios arise. The first is that in the limit $μ\to \infty$ the first-order line ends in a critical point; the second is a change in the nature of the transition at some finite chemical potential; the third is that the entire line is one of continuous phase transitions. Results from other ALG models and the fact that mean-field approximations show a discontinuous phase transition for the three-state Potts model (known to possess a continuous transition) lends some weight to the third alternative.

cond-mat.stat-mech↗

arXiv2018

Kardar-Parisi-Zhang growth on one-dimensional decreasing substrates

Recent experimental works on one-dimensional (1D) circular Kardar-Parisi-Zhang (KPZ) systems whose radii decrease in time have reported controversial conclusions about the statistics of their interfaces. Motivated by this, we investigate here several 1D KPZ models on substrates whose size changes in time as $L(t)=L_0 + ωt$, focusing on the case $ω<0$. From extensive numerical simulations, we show that for $L_0 \gg 1$ there exists a transient regime in which the statistics is consistent with that of flat KPZ systems (the $ω=0$ case), for both $ω<0$ and $ω>0$. Actually, for a given model, $L_0$ and $|ω|$, we observe that a difference between ingrowing ($ω<0$) and outgrowing ($ω>0$) systems arises only at long times ($t \gtrsim t_c=L_0/|ω|$), when the expanding surfaces cross over to the statistics of curved KPZ systems, whereas the shrinking ones become completely correlated. A generalization of the Family-Vicsek scaling for the roughness of ingrowing interfaces is presented. Our results demonstrate that a transient flat statistics is a general feature of systems starting with large initial sizes, regardless their curvature. This is consistent with their recent observation in ingrowing turbulent liquid crystal interfaces, but it is in contrast with the apparent observation of curved statistics in colloidal deposition at the edge of evaporating drops. A possible explanation for this last result, as a consequence of the very small number of monolayers analyzed in this experiment, is given. This is illustrated in a competitive growth model presenting a few-monolayer transient and an asymptotic behavior consistent, respectively, with the curved and flat statistics.

cond-mat.stat-mech↗

arXiv2017

Collapse transition in polymer models with multiple monomers per site and multiple bonds per edge

We present results from extensive Monte Carlo simulations of polymer models where each lattice site can be visited by up to $K$ monomers and no restriction is imposed on the number of bonds on each lattice edge. These \textit{multiple monomer per site} (MMS) models are investigated on the square and cubic lattices, for $K=2$ and $K=3$, by associating Boltzmann weights $ω_0=1$, $ω_1=e^{β_1}$ and $ω_2=e^{β_2}$ to sites visited by 1, 2 and 3 monomers, respectively. Two versions of the MMS models are considered for which immediate reversals of the walks are allowed (RA) or forbidden (RF). In contrast to previous simulations of these models, we find the same thermodynamic behavior for both RA and RF versions. In three-dimensions, the phase diagrams - in space $β_2 \times β_1$ - are featured by coil and globule phases separated by a line of $Θ$ points, as thoroughly demonstrated by the metric $ν_t$, crossover $ϕ_t$ and entropic $γ_t$ exponents. The existence of the $Θ$-lines is also confirmed by the second virial coefficient. This shows that no discontinuous collapse transition exists in these models, in contrast to previous claims based on a weak bimodality observed in some distributions, which indeed exists in a narrow region very close to the $Θ$-line when $β_1 < 0$. Interestingly, in two-dimensions, only a crossover is found between the coil and globule phases.

cond-mat.soft↗

arXiv2017

Solution of semi-flexible self-avoiding trails on a Husimi lattice built with squares

We study a model of semi-flexible self-avoiding trails, where the lattice paths are constrained to visit each lattice edge at most once, with configurations weighted by the number of collisions, crossings and bends, on a Husimi lattice built with squares. We find a rich phase diagram with five phases: a non-polymerised phase (${\bf NP}$), low density (${\bf P1}$) and high density (${\bf P2}$) polymerised phases, and, for sufficiently large stiffness, two additional anisotropic (nematic) (${\bf AN1}$ and ${\bf AN2}$) polymerised phases within the ${\bf P1}$ phase. Moreover, the {\bf AN1} phase which shows a broken symmetry with a preferential direction, is separated from the ${\bf P1}$ phase by the other nematic ${\bf AN2}$ phase. Although this scenario is similar to what was found in our previous calculation on the Bethe lattice, where the ${\bf AN-P1}$ transition was discontinuous and critical, the presence of the additional nematic phase between them introduces a qualitative difference. Other details of the phase diagram are that a line of tri-critical points may separate the ${\bf P1}-{\bf P2}$ transition surface into a continuous and a discontinuous portion, and that the same may happen at the ${\bf NP}-{\bf P1}$ transition surface, details of which depend on whether crossings are allowed or forbidden. A critical end-point line is also found in the phase diagram.

cond-mat.stat-mech↗

arXiv2016

Polymers with nearest- and next nearest-neighbor interactions on the Husimi lattice

The exact grand-canonical solution of a generalized interacting self-avoid walk (ISAW) model, placed on a Husimi lattice built with squares, is presented. In this model, beyond the traditional interaction $ω_1=e^{ε_1/k_B T}$ between (nonconsecutive) monomers on nearest-neighbor (NN) sites, an additional energy $ε_2$ is associated to next-NN (NNN) monomers. Three definitions of NNN sites/interactions are considered, where each monomer can have, effectively, at most 2, 4 or 6 NNN monomers on the Husimi lattice. The phase diagrams found in all cases have (qualitatively) the same thermodynamic properties: a non-polymerized (NP) and a polymerized (P) phase separated by a critical and a coexistence surface that meet at a tricritical ($θ$-) line. This $θ$-line is found even when one of the interactions is repulsive, existing for $ω_1$ in the range $[0,\infty)$, i. e., for $ε_1/k_B T$ in the range $[-\infty,\infty)$. Counterintuitively, a $θ$-point exists even for an infinite repulsion between NN monomers ($ω_1=0$), being associated to a coil-"soft globule" transition. In the limit of an infinite repulsive force between NNN monomers, however, the coil-globule transition disappears and only a NP-P continuous transition is observed. This particular case, with $ω_2=0$, is also solved exactly on the square lattice, using a transfer matrix calculation, where a discontinuous NP-P transition is found. For attractive and repulsive forces between NN and NNN monomers, respectively, the model becomes quite similar to the semiflexible-ISAW one, whose crystalline phase is not observed here, as a consequence of the frustration due to competing NN and NNN forces. The mapping of the phase diagrams in canonical ones is discussed and compared with recent results from Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2015

Nature of the collapse transition in interacting self-avoiding trails

We study the interacting self-avoiding trail (ISAT) model on a Bethe lattice of general coordination $q$ and on a Husimi lattice built with squares and coordination $q=4$. The exact grand-canonical solutions of the model are obtained, considering that up to $K$ monomers can be placed on a site and associating a weight $ω_i$ for a $i$-fold visited site. Very rich phase diagrams are found with non-polymerized (NP), regular polymerized (P) and dense polymerized (DP) phases separated by lines (or surfaces) of continuous and discontinuous transitions. For Bethe lattice with $q=4$ and $K=2$, the collapse transition is identified with a bicritical point and the collapsed phase is associated to the dense polymerized phase (solid-like) instead of the regular polymerized phase (liquid-like). A similar result is found for the Husimi lattice, which may explain the difference between the collapse transition for ISAT's and for interacting self-avoiding walks on the square lattice. For $q=6$ and $K=3$ (studied on the Bethe lattice only), a more complex phase diagram is found, with two critical planes and two coexistence surfaces, separated by two tricritical and two critical end-point lines meeting at a multicritical point. The mapping of the phase diagrams in the canonical ensemble is discussed and compared with simulational results for regular lattices.

cond-mat.stat-mech↗

arXiv2014

On the origins of scaling corrections in ballistic growth models

We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes strong corrections to the scaling, comes from the fluctuations in the height increments along deposition events. Accounting for this correction in the scaling analysis, we obtained scaling exponents in excellent agreement with the KPZ class. We also propose a method to suppress these corrections, which consists in divide the surface in bins of size $\varepsilon$ and use only the maximal height inside each bin to do the statistics. Again, scaling exponents in remarkable agreement with the KPZ class were found. The binning method allowed the accurate determination of the height distributions of the ballistic models in both growth and steady state regimes, providing the universal underlying fluctuations foreseen for KPZ class in 2+1 dimensions. Our results provide complete and conclusive evidences that the ballistic model belongs to the KPZ universality class in $2+1$ dimensions. Potential applications of the methods developed here, in both numerics and experiments, are discussed.

cond-mat.stat-mech↗

arXiv2014

Monte Carlo simulations of polymers with nearest- and next nearest-neighbor interactions on square and cubic lattices

We study a generalized interacting self-avoiding walk (ISAW) model with nearest- and next nearest-neighbor (NN and NNN) interactions on the square and cubic lattices. In both dimensions, the phase diagrams show coil and globule phases separated by continuous transition lines. Along these lines, we calculate the metric $ν_t$, crossover $ϕ_t$ and entropic $γ_t$ exponents, all of them in good agreement with the exact values of the $Θ$ universality class. Therefore, the introduction of NNN interactions does not change the class of the ISAW model, which still exists even for repulsive forces. The growth parameters $μ_t$ are shown to change monotonically with temperature along the $Θ$-lines. In the square lattice, the $Θ$-line has an almost linear behavior, which was not found in the cubic one. Although the region of repulsive NNN interactions, with attractive NN ones, leads to stiff polymers, no evidence of a transition to a crystalline phase was found.

cond-mat.soft↗

arXiv2014

Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension

We show that the theoretical machinery developed for the Kardar-Parisi-Zhang (KPZ) class in low dimensions are obeyed by the restricted solid-on-solid (RSOS) model for substrates with dimensions up to $d=6$. Analyzing different restriction conditions, we show that height distributions of the interface are universal for all investigated dimensions. It means that fluctuations are not negligible and, consequently, the system is still below the upper critical dimension at $d=6$. The extrapolation of the data to dimensions $d\ge7$ predicts that the upper critical dimension of the KPZ class is infinite.

cond-mat.stat-mech↗

arXiv2013

Non-universal parameters, corrections and universality in Kardar-Parisi-Zhang growth

We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d=1+1, for both flat and curved geometries. We analyzed two classes of models. In the isotropic models the non-universal parameters are uniform along the surface, whereas in the anisotropic growth they vary. In the latter case, that produces curved surfaces, the statistics must be computed independently along fixed directions. The ansatz h = v t + (Γt)^{1/3} χ+ η, where χis a Tracy-Widom (geometry-dependent) distribution and ηis a time-independent correction, is probed. Our numerical analysis shows that the non-universal parameter Γdetermined through the first cumulant leads to a very good accordance with the extended KPZ ansatz for all investigated models in contrast with the estimates of Γobtained from higher order cumulants that indicate a violation of the generalized ansatz for some of the studied models. We associate the discrepancies to corrections of unknown nature, which hampers an accurate estimation of Γat finite times. The discrepancies in Γvia different approaches are relatively small but sufficient to modify the scaling law t^{-1/3} that characterize the finite-time corrections due to η. Among the investigated models, we have revisited an off-lattice Eden model that supposedly disobeyed the shift in the mean scaling as t^{-1/3} and showed that there is a crossover to the expected regime. We have found model-dependent (non-universal) corrections for cumulants of order n > 1. All investigated models are consistent with a further term of order t^{-1/3} in the KPZ ansatz.

cond-mat.stat-mech↗

arXiv2013

Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections

The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different from their Tracy-Widom counterpart in one-dimension, were found. Distributions exhibit finite-time corrections hallmarked by a shift in the mean decaying as t^-β, where βis the growth exponent. Our results support a generalization of the ansatz h = v t + (Γt)^βχ+ η+ ζt^-βto higher dimensions, where v, Γ, ζand ηare non-universal quantities whereas βand χare universal and the last one depends on the surface geometry. Generalized Gumbel distributions provide very good fits of the distributions in at least four orders of magnitude around the peak, which can be used for comparisons with experiments. Our numerical results call for analytical approaches and experimental realizations of KPZ class in two-dimensional systems.

cond-mat.stat-mech↗

arXiv2013

Height distributions in competitive one-dimensional Kardar-Parisi-Zhang systems

We study the competitive RSOS-BD model focusing on the validity of the Kardar-Parisi-Zhang (KPZ) ansatz h(t) = v t + (Γt)^β χand the universality of the height distributions (HDs) near the point where the model has Edwards-Wilkinson (EW) scaling. Using numerical simulations for long times, we show that the system is asymptotically KPZ, as expected, for values of the probability of the RSOS component very close to p = p_c \approx 0.83. Namely, the growth exponents converge to β_{KPZ} = 1/3 and the HDs converge to the GOE Tracy-Widom distribution, however, the convergence seems to be faster in the last ones. While the EW-KPZ crossover appears in the roughness scaling in a broad range of probabilities p around p_c, a Gaussian-GOE crossover is not observed in the HDs into the same interval, possibly being restricted to values of p very close to p_c. These results improve recent ones reported by de Assis et al. [Phys. Rev. E 86, 051607 (2012)], where, based on smaller simulations, the KPZ scaling was argued to breakdown in broad range of p around p_c.

cond-mat.stat-mech↗