arXiv subjects

André P. Vieira

Publications and source records attributed to André P. Vieira.

15 recordsLinked to original sources

arXiv2025

Exact Mapping of Nonequilibrium to Equilibrium Phase Transitions for Systems in Contact with Two Thermal Baths

We show that a large class of nonequilibrium many-body systems in contact with two thermal baths admit an exact mapping onto equivalent equilibrium systems. This mapping provides direct access to nonequilibrium phase transition points from known equilibrium results, irrespective of the model, interaction topology, or distance from equilibrium. We verify the universality of this correspondence using paradigmatic models (Ising, Potts, and Blume-Capel), and highlight distinctive features in entropy production close to critical and tricritical points. Our findings connect equilibrium and nonequilibrium statistical mechanics, with implications for microscopic thermal machines and stochastic thermodynamics.

cond-mat.stat-mech↗

arXiv2024

Splitting of nonequilibrium phase transitions in driven Ising models

Spontaneous symmetry breaking occurs in various equilibrium and nonequilibrium systems, where phase transitions are typically marked by a single critical point that separates ordered and disordered regimes. We reveal a novel phenomenon in which the interplay between different temperatures and driving forces splits the order-disorder transition into two distinct transition points depending on which ordered state initially dominates. Crucially, these two emerging phases have distinct scaling behaviors and thermodynamic properties. To study this, we propose a minimal variant of the Ising model where spins are coupled to two thermal baths and subjected to two opposite driving forces associated to them. Our findings, robust both for all-to-all interactions (where exact solutions are possible) and nearest-neighbor couplings on a square lattice, uncover unique nonequilibrium behaviors and scaling laws for crucial thermodynamic quantities, such as efficiency, dissipation, power and its fluctuations, that are different between the two ordered phases. We also highlight that one of these emerging phases enables heat-engine operations that are less dissipative and show reduced fluctuations. In this setup, the system can also operate near maximum power and efficiency over a wide parameter range. Our results offer new insights into the relevance of phase transitions under nonequilibrium conditions.

cond-mat.stat-mech↗

arXiv2024

Mean-field model for a mixture of biaxial nematogens and dipolar nanoparticles

We analyze a mean-field model for mixtures involving biaxial nematogens and dipolar nanoparticles, taking into account orientational and isotropic pair interactions between nematogens, but also orientational nematogen-nanoparticle interactions. We determine bulk equilibrium phase diagrams for a wide range of interaction strengths, identifying in each case the effect of the nanoparticles on the stability of nematic phases and on the appearance of multicritical points. Special attention is given to the limit of low concentration of nanoparticles, in which their effect on the temperatures of both the first-order uniaxial-isotropic and the continuous biaxial-uniaxial transitions is investigated in detail.

cond-mat.soft↗

arXiv2023

Contact process with aperiodic temporal disorder

We investigate the nonequilibrium critical behavior of the contact process with deterministic aperiodic temporal disorder implemented by choosing healing or infection rates according to a family of aperiodic sequences based on the quasiperiodic Fibonacci sequence. This family allows us to gauge the temporal fluctuations via a wandering exponent $ω$ and put our work in the context of the Kinzel--Vojta--Dickman criterion for the relevance of temporal disorder to the critical behavior of nonequilibrium models. By means of analytic and numerical calculations, the generalized criterion is tested in the mean-field limit.

cond-mat.stat-mech↗

arXiv2020

Quantum coherence and criticality in irreversible work

The irreversible work during a driving protocol constitutes one of the most widely studied measures in non-equilibrium thermodynamics, as it constitutes a proxy for entropy production. In quantum systems, it has been shown that the irreversible work has an additional, genuinely quantum mechanical contribution, due to coherence produced by the driving protocol. The goal of this paper is to explore this contribution in systems that undergo a quantum phase transition. Substantial effort has been dedicated in recent years to understand the role of quantum criticality in work protocols. However, practically nothing is known about how coherence contributes to it. To shed light on this issue, we study the entropy production in infinitesimal quenches of the one-dimensional XY model. For quenches in the transverse field, we find that for finite temperatures the contribution from coherence can, in certain cases, account for practically all of the entropy production. At low temperatures, however, the coherence presents a finite cusp at the critical point, whereas the entropy production diverges logarithmically. Alternatively, if the quench is performed in the anisotropy parameter, we find that there are situations where all of the entropy produced is due to quantum coherences.

quant-ph↗

arXiv2018

Percolation on Isotropically Directed Lattice

We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We derive exact results for the percolation threshold on planar lattices, and present a conjecture for the value the percolation-threshold for in any lattice. We also identify presumably universal critical exponents, including a fractal dimension, associated with the strongly-connected components both for planar and cubic lattices. These critical exponents are different from those associated either with standard percolation or with directed percolation.

cond-mat.dis-nn↗

arXiv2018

Emergent dimerization and localization in disordered quantum chains

We uncover a novel mechanism for inducing a gapful phase in interacting many-body quantum chains. The mechanism is nonperturbative, being triggered only in the presence of both strong interactions and strong aperiodic (disordered) modulation. In the context of the critical antiferromagnetic spin-1/2 XXZ chain, we identify an emerging dimerization which removes the system from criticality and stabilizes the novel phase. This mechanism is shown to be quite general in strongly interacting quantum chains in the presence of strongly modulated quasiperiodic disorder which is, surprisingly, perturbatively irrelevant. Finally, we also characterize the associated quantum phase transition via the corresponding critical exponents and thermodynamic properties.

cond-mat.str-el↗

arXiv2016

A mesoscopic approach to subcritical fatigue crack growth

We investigate a model for fatigue crack growth in which damage accumulation is assumed to follow a power law of the local stress amplitude, a form which can be generically justified on the grounds of the approximately self-similar aspect of microcrack distributions. Our aim is to determine the relation between model ingredients and the Paris exponent governing subcritical crack-growth dynamics at the macroscopic scale, starting from a single small notch propagating along a fixed line. By a series of analytical and numerical calculations, we show that, in the absence of disorder, there is a critical damage-accumulation exponent $γ$, namely $γ_c=2$, separating two distinct regimes of behavior for the Paris exponent $m$. For $γ>γ_c$, the Paris exponent is shown to assume the value $m=γ$, a result which proves robust against the separate introduction of various modifying ingredients. Explicitly, we deal here with (i) the requirement of a minimum stress for damage to occur; (ii) the presence of disorder in local damage thresholds; (iii) the possibility of crack healing. On the other hand, in the regime $γ<γ_c$ the Paris exponent is seen to be sensitive to the different ingredients added to the model, with rapid healing or a high minimum stress for damage leading to $m=2$ for all $γ<γ_c$, in contrast with the linear dependence $m=6-2γ$ observed for very long characteristic healing times in the absence of a minimum stress for damage. Upon the introduction of disorder on the local fatigue thresholds, which leads to the possible appearance of multiple cracks along the propagation line, the Paris exponent tends to $m\approx 4$ for $γ\lesssim 2$, while retaining the behavior $m=γ$ for $γ\gtrsim 4$.

cond-mat.dis-nn↗

arXiv2012

Fatigue in disordered media

We obtain the Paris law of fatigue crack propagation in a disordered solid using a fuse network model where the accumulated damage in each resistor increases with time as a power law of the local current amplitude. When a resistor reaches its fatigue threshold, it burns irreversibly. Over time, this drives cracks to grow until the system is fractured in two parts. We study the relation between the macroscopic exponent of the crack growth rate -- entering the phenomenological Paris law -- and the microscopic damage-accumulation exponent, $γ$, under the influence of disorder. The way the jumps of the growing crack, $Δa$, and the waiting-time between successive breaks, $Δt$, depend on the type of material, via $γ$, are also investigated. We find that the averages of these quantities, $<Δa>$ and $<Δt>/ $, scale as power laws of the crack length $a$, $<Δa> \propto a^α$ and $<Δt>/ \propto a^{-β}$, where $ $ is the average rupture time. Strikingly, our results show, for small values of $γ$, a decrease in the exponent of the Paris law in comparison with the homogeneous case, leading to an increase in the lifetime of breaking materials. For the particular case of $γ=0$, when fatigue is exclusively ruled by disorder, an analytical treatment confirms the results obtained by simulation.

cond-mat.mtrl-sci↗

arXiv2012

Strong disorder renormalization group study of aperiodic quantum Ising chains

We employ an adaptation of a strong-disorder renormalization-group technique in order to analyze the ferro-paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse field. In the presence of marginal or relevant geometric fluctuations induced by aperiodicity, for which the critical behavior is expected to depart from the Onsager universality class, we derive analytical and asymptotically exact expressions for various critical exponents (including the correlation-length and the magnetization exponents, which are not easily obtainable by other methods), and shed light onto the nature of the ground state structures in the neighborhood of the critical point. The main results obtained by this approach are confirmed by finite-size scaling analyses of numerical calculations based on the free-fermion method.

cond-mat.stat-mech↗

arXiv2008

Subcritical crack growth: the microscopic origin of Paris's law

We investigate the origin of Paris's law, which states that the velocity of a crack at subcritical load grows like a power law, $da/dt \sim (ΔK)^{m}$, where $ΔK$ is the stress intensity factor amplitude. Starting from a damage accumulation function proportional to $(Δσ)^γ$, $Δσ$ being the stress amplitude, we show analytically that the asymptotic exponent $m$ can be expressed as a piecewise-linear function of the %damage accumulation exponent $γ$, namely, $m=6-2γ$ for $γ< γ_{c}$, and $m=γ$ for $γ\ge γ_{c}$, reflecting the existence of a critical value $γ_{c}=2$. %In this way, here we discover the existence of a critical %value $γ_{c}=2$ characterized by a scaling law with a critical %exponent separating two regimes of different linear functions $m %(γ)$. We performed numerical simulations to confirm this result for finite sizes. Finally, we introduce bounded disorder in the breaking thresholds and find that below $γ_{c}$ disorder is relevant, i.e., the exponent $m$ is changed, while above $γ_{c}$ disorder is irrelevant.

cond-mat.mtrl-sci↗

arXiv2007

Correlation amplitude and entanglement entropy in random spin chains

Using strong-disorder renormalization group, numerical exact diagonalization, and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ spin-1/2 chain focusing on the long-length and ground-state behavior of the average time-independent spin-spin correlation function C(l)=\upsilon l^{-η}. In addition to the well-known universal (disorder-independent) power-law exponent η=2, we find interesting universal features displayed by the prefactor \upsilon=\upsilon_o/3, if l is odd, and \upsilon=\upsilon_e/3, otherwise. Although \upsilon_o and \upsilon_e are nonuniversal (disorder dependent) and distinct in magnitude, the combination \upsilon_o + \upsilon_e = -1/4 is universal if C is computed along the symmetric (longitudinal) axis. The origin of the nonuniversalities of the prefactors is discussed in the renormalization-group framework where a solvable toy model is considered. Moreover, we relate the average correlation function with the average entanglement entropy, whose amplitude has been recently shown to be universal. The nonuniversalities of the prefactors are shown to contribute only to surface terms of the entropy. Finally, we discuss the experimental relevance of our results by computing the structure factor whose scaling properties, interestingly, depend on the correlation prefactors.

cond-mat.dis-nn↗

arXiv2007

Analytical approach to directed sandpile models on the Apollonian network

We investigate a set of directed sandpile models on the Apollonian network, which are inspired on the work by Dhar and Ramaswamy (PRL \textbf{63}, 1659 (1989)) for Euclidian lattices. They are characterized by a single parameter $q$, that restricts the number of neighbors receiving grains from a toppling node. Due to the geometry of the network, two and three point correlation functions are amenable to exact treatment, leading to analytical results for the avalanche distributions in the limit of an infinite system, for $q=1,2$. The exact recurrence expressions for the correlation functions are numerically iterated to obtain results for finite size systems, when larger values of $q$ are considered. Finally, a detailed description of the local flux properties is provided by a multifractal scaling analysis.

cond-mat.stat-mech↗

arXiv2005

Aperiodic quantum XXZ chains: Renormalization-group results

We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations of chains with couplings following several two-letter aperiodic sequences, including the quasiperiodic Fibonacci and other precious-mean sequences, as well as sequences inducing strong geometrical fluctuations. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly-known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. We also discuss the nature of the ground-state structures, and their comparison with the random-singlet phase, characteristic of random-bond chains.

cond-mat.str-el↗

arXiv2005

Low-energy properties of aperiodic quantum spin chains

We investigate the low-energy properties of antiferromagnetic quantum XXZ spin chains with couplings following two-letter aperiodic sequences, by an adaptation of the Ma-Dasgupta-Hu renormalization-group method. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. As representative illustrations, we present analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations for couplings following the Fibonacci quasiperiodic structure and a binary Rudin-Shapiro sequence, whose geometrical fluctuations are similar to those induced by randomness.

cond-mat.str-el↗