We study classical spin models on the 1/1 Tsai-type approximant lattice using Monte Carlo and mean-field methods. Our aim is to understand whether the phase diagram differences between Gd- and Tb-based approximants ca...
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We study classical spin models on the 1/1 Tsai-type approximant lattice using Monte Carlo and mean-field methods. Our aim is to understand whether the phase diagram differences between Gd- and Tb-based approximants can be attributed to anisotropy induced by the crystal-electric field. To address this question, we treat Gd ions as Heisenberg spins and Tb ions as Ising spins. Additionally, we consider the presence of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction to replicate the experimentally observed correlation between magnetic properties and electron concentration. Surprisingly, our findings show that the transition between ferromagnetic and antiferromagnetic order remains unaltered by the anisotropy, even when accounting for the dipole interaction. We conclude that a more comprehensive model, extending beyond the free-electron gas RKKY interaction, is likely required to fully understand the distinctions between Gd- and Tb-based approximants. Our work represents a systematic exploration of the impact of anisotropy on the ground-state properties of classical spin models in quasicrystal approximants.
Heider's structural balance theory has proven invaluable in comprehending the dynamics of social groups characterized by both friendly and hostile relationships. Since people's relations are rarely single face...
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Heider's structural balance theory has proven invaluable in comprehending the dynamics of social groups characterized by both friendly and hostile relationships. Since people's relations are rarely single faceted, we investigate Heider balance dynamics on a multiplex network, consisting of several copies of the same agent displaying correlated relations at different layers building the multiplex. Intralayer interactions in our model adhere to Heider dynamics, while interlayer correlations stem from Ising interactions, with the heat-bath dynamics of link signs. Our investigation reveals a multifaceted system with a diverse equilibrium landscape contingent on the coexistence of distinct phases across layers. We observe that, starting from a paradise state with positive links in all layers, an increase in temperature triggers a discontinuous transition to a disordered state akin to single-layer scenarios. The critical temperature surpasses that of the single-layer case, a fact verified through extended mean-field analysis and agent-based simulations. Furthermore, the scenario shifts when one layer exhibits a two-clique configuration instead of a paradise state. This change introduces additional transitions: synchronization of interlayer relations and a transition to the disorder, appearing at a different, lower temperature compared to matching paradise states. This exploration shows the intricate interplay of Heider balance and multiplex interactions.
作者:
Celeste MendesGloria M. BuendíaPer Arne RikvoldDepartment of Physics
<a href="https://***/01ak5cj98">Universidad Simón Bolívar</a> Caracas 1080 Venezuela. PoreLab
NJORD Centre Department of Physics <a href="https://***/01xtthb56">University of Oslo</a> P.O. Box 1048 Blindern 0316 Oslo Norway and Department of Physics <a href="https://***/05g3dte14">Florida State University</a> Tallahassee Florida 32306-4350 USA.
We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods [P. Riego et al., Phys. Re...
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We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods [P. Riego et al., Phys. Rev. Lett. 118, 117202 (2017); G. M. Buendía et al., Phys. Rev. B 96, 134306 (2017)]. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of ±1,0, with a nonzero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multidroplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model [M. Schick et al., Phys. Rev. B 34, 1797 (1986)]. Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the crit
Aging in phase-ordering kinetics of the d=3 Ising model following a quench from infinite to zero temperature is studied by means of Monte Carlo simulations. In this model the two-time spin-spin autocorrelator Cag is e...
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Aging in phase-ordering kinetics of the d=3 Ising model following a quench from infinite to zero temperature is studied by means of Monte Carlo simulations. In this model the two-time spin-spin autocorrelator Cag is expected to obey dynamical scaling and to follow asymptotically a power-law decay with the autocorrelation exponent λ. Previous work indicated that the lower Fisher-Huse bound of λ≥d/2=1.5 is violated in this model. Using much larger systems than previously studied, the instantaneous exponent for λ we obtain at late times does not disagree with this bound. By conducting systematic fits to the data of Cag using different Ansätze for the leading correction term, we find λ=1.58(14), with most of the error attributed to the systematic uncertainty regarding the Ansätze. This result is in contrast to the recent report that below the roughening transition universality might be violated.
Many systems, when initially placed far from equilibrium, exhibit surprising behavior in their attempt to equilibrate. Striking examples are the Mpemba effect and the cooling-heating asymmetry. These anomalous behavio...
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Many systems, when initially placed far from equilibrium, exhibit surprising behavior in their attempt to equilibrate. Striking examples are the Mpemba effect and the cooling-heating asymmetry. These anomalous behaviors can be exploited to shorten the time needed to cool down (or heat up) a system. Though, a strategy to design these effects in mesoscopic systems is missing. We bring forward a description that allows us to formulate such strategies, and, along the way, makes natural these paradoxical behaviors. In particular, we study the evolution of macroscopic physical observables of systems freely relaxing under the influence of one or two instantaneous thermal quenches. The two crucial ingredients in our approach are timescale separation and a nonmonotonic temperature evolution of an important state function. We argue that both are generic features near a first-order transition. Our theory is exemplified with the one-dimensional Ising model in a magnetic field using analytic results and numerical experiments.
We study the de Almeida–Thouless (AT) line in the one-dimensional power-law diluted XY spin-glass model, in which the probability that two spins separated by a distance r interact with each other, decays as 1/r2σ. T...
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We study the de Almeida–Thouless (AT) line in the one-dimensional power-law diluted XY spin-glass model, in which the probability that two spins separated by a distance r interact with each other, decays as 1/r2σ. Tuning the exponent σ is equivalent to changing the space dimension of a short-range model. We develop a heat bath algorithm to equilibrate XY spins; using this in conjunction with the standard parallel tempering and overrelaxation sweeps, we carry out large-scale Monte Carlo simulations. For σ=0.6, which is in the mean-field regime above six dimensions—it is similar to being in 10 dimensions—we find clear evidence for an AT line. For σ=0.75 and σ=0.85, which are in the non-mean-field regime and similar to four and three dimensions, respectively, our data is like that found in previous studies of the Ising and Heisenberg spin glasses when reducing the temperature at fixed field. For σ=0.75, there is evidence from finite-size-scaling studies for an AT transition but for σ=0.85, the evidence for a transition is nonexistent. We have also studied these systems at fixed temperature varying the field and discovered that at both σ=0.75 and at σ=0.85 there is evidence of an AT transition! Confusingly, the correlation length and spin-glass susceptibility as a function of the field are both entirely consistent with the predictions of the droplet picture and hence the nonexistence of an AT line. In the usual finite-size critical point scaling studies used to provide evidence for an AT transition, there is seemingly good evidence for an AT line at σ=0.75 for small values of the system size N, which is strengthening as N is increased, but for N>2048 the trend changes and the evidence then weakens as N is further increased. We have also studied with fewer bond realizations the system at σ=0.70, which is the analog of a system with short-range interactions just below six dimensions, and found that it is similar in its behavior to the system at σ=0.75 but with larger fini
We investigate two concrete cases of phase transitions breaking a subsystem symmetry. The models are two classical compass models featuring line-flip and plane-flip symmetries and correspond to special limits of a Hei...
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We investigate two concrete cases of phase transitions breaking a subsystem symmetry. The models are two classical compass models featuring line-flip and plane-flip symmetries and correspond to special limits of a Heisenberg-Kitaev Hamiltonian on a cubic lattice. We show that these models experience a hybrid symmetry breaking by which the system display distinct symmetry broken patterns in different submanifolds. For instance, the system may look magnetic within a chain or plane but nematic-like when observing from one dimensionality higher. We fully characterize the symmetry-broken phases by a set of subdimensional order parameters and confirm numerically both cases undergo a non-standard first-order phase transition. Our results provide new insights into phase transitions involving subsystem symmetries and generalize the notion of conventional spontaneous symmetry breaking.
In this paper, we develop the self-learning Monte-Carlo (SLMC) algorithm for non-Abelian gauge theory with dynamical fermions in four dimensions to resolve the autocorrelation problem in lattice QCD. We perform simula...
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In this paper, we develop the self-learning Monte-Carlo (SLMC) algorithm for non-Abelian gauge theory with dynamical fermions in four dimensions to resolve the autocorrelation problem in lattice QCD. We perform simulations with the dynamical staggered fermions and plaquette gauge action by both in the hybrid Monte-Carlo (HMC) and SLMC for zero and finite temperature to examine the validity of SLMC. We confirm that SLMC can reduce autocorrelation time in non-Abelian gauge theory and reproduce results from HMC. For finite temperature runs, we confirm that SLMC reproduces correct results with HMC, including higher-order moments of the Polyakov loop and the chiral condensate. Besides, our finite temperature calculations indicate that four flavor QC2D with m^=0.5 is likely in the crossover regime in the Colombia plot.
When studied at finite temperature, Yang-Mills theories in 3+1 dimensions display the presence of confinement/deconfinement phase transitions, which are known to be of first order—the SU(2) gauge theory being the exc...
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When studied at finite temperature, Yang-Mills theories in 3+1 dimensions display the presence of confinement/deconfinement phase transitions, which are known to be of first order—the SU(2) gauge theory being the exception. Theoretical as well as phenomenological considerations indicate that it is essential to establish a precise characterization of these physical systems in proximity of such phase transitions. We present and test a new method to study the critical region of parameter space in non-Abelian quantum field theories on the lattice, based upon the logarithmic linear relaxation (LLR) algorithm. We apply this method to the SU(3) Yang-Mills lattice gauge theory, and perform extensive calculations with one fixed choice of lattice size. We identify the critical temperature, and measure interesting physical quantities near the transition. Among them, we determine the free energy of the model in the critical region, exposing for the first time its multivalued nature with a numerical calculation from first principles, providing this novel evidence in support of a first-order phase transition. This study sets the stage for future high-precision measurements, by demonstrating the potential of the method.
We study a Heisenberg-Dzyaloshinskĭ-Moriya Hamiltonian on AB-stacked kagome bilayers at finite temperature. In a large portion of the parameter space, we observe three qualitative changes upon cooling the system: a cr...
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We study a Heisenberg-Dzyaloshinskĭ-Moriya Hamiltonian on AB-stacked kagome bilayers at finite temperature. In a large portion of the parameter space, we observe three qualitative changes upon cooling the system: a crossover from a Heisenberg paramagnet to an XY chiral paramagnet, a Kosterlitz-Thouless transition to a chiral nematic phase, and a fluctuation-induced first-order transition to an Ising-like phase. We characterize the properties of phases numerically using Monte Carlo finite-size analysis. To further explain the nature of the observed phase transitions, we develop an analytical coarse-graining procedure that maps the Hamiltonian onto a generalized XY model on a triangular lattice. To leading order, this effective model includes both bilinear and biquadratic interactions and is able to correctly predict the two phase transitions. Lastly, we study the Ising fluctuations at low temperatures and establish that the origin of the first-order transition stems from the quasidegenerate ring manifold in the momentum space.
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