We prove duality relations for two interacting particle systems: the q-deformed totally asymmetric simple exclusion process (q-TASEP) and the asymmetric simple exclusion process (ASEP). Expectations ...of the duality functionals correspond to certain joint moments of particle locations or integrated currents, respectively. Duality implies that they solve systems of ODEs. These systems are integrable and for particular step and half-stationary initial data we use a nested contour integral ansatz to provide explicit formulas for the systems' solutions, and hence also the moments. We form Laplace transform-like generating functions of these moments and via residue calculus we compute two different types of Fredholm determinant formulas for such generating functions. For ASEP, the first type of formula is new and readily lends itself to asymptotic analysis (as necessary to reprove GUE Tracy–Widom distribution fluctuations for ASEP), while the second type of formula is recognizable as closely related to Tracy and Widom's ASEP formula Comm. Math. Phys. 279 (2008) 815–844, J. Stat. Phys. 132 (2008) 291–300, Comm. Math. Phys. 290 (2009) 129–154, J. Stat. Phys. 140 (2010) 619–634. For q-TASEP, both formulas coincide with those computed via Borodin and Corwin's Macdonald processes Probab. Theory Related Fields (2014) 158 225–400. Both q-TASEP and ASEP have limit transitions to the free energy of the continuum directed polymer, the logarithm of the solution of the stochastic heat equation or the Hopf–Cole solution to the Kardar–Parisi–Zhang equation. Thus, q-TASEP and ASEP are integrable discretizations of these continuum objects; the systems of ODEs associated to their dualities are deformed discrete quantum delta Bose gases; and the procedure through which we pass from expectations of their duality functionals to characterizing generating functions is a rigorous version of the replica trick in physics.
The Kardar–Parisi–Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but ...a few. Since the year 2000, our understanding of the one-dimensional KPZ class has been completely renewed by mathematical physics approaches based on exact solutions. Mathematical physics has played a central role since then, leading to a myriad of new developments, but their implications are clearly not limited to mathematics — as a matter of fact, it can also be studied experimentally. The aim of these lecture notes is to provide an introduction to the field that is accessible to non-specialists, reviewing basic properties of the KPZ class and highlighting main physical outcomes of mathematical developments since the year 2000. It is written in a brief and self-contained manner, with emphasis put on physical intuitions and implications, while only a small (and mostly not the latest) fraction of mathematical developments could be covered. Liquid-crystal experiments by the author and coworkers are also reviewed.
•A review on recent developments on KPZ, intended for non-specialists, is given.•Physical implications of theoretical results are stressed.•Connections to directed polymer, a quantum many-body system, etc. are explained.•Experimental study using liquid-crystal turbulence is also explained.
We present here results on the determination of the critical temperature in the chiral limit for (2+1)-flavor QCD. We propose two novel estimators of the chiral critical temperature where quark mass ...dependence is strongly suppressed compared to the conventional estimator using pseudo-critical temperatures. We have used the HISQ/tree action for the numerical simulation with lattices with three different temporal extent Nτ = 6, 8, 12 and varied the aspect ratio over the range 4≤Nσ/Nτ≤8. To approach the chiral limit, the light quark mass has been decreased keeping the strange quark mass fixed at its physical value. Our simulations correspond to the range of pion masses, 55MeV≤mπ≤160MeV.
The previously reported X2O3 (X=V, Cr, Mn, Ta) monolayers crystallize in a honeycomb–kagome (HK) structure and are found primarily to be ferromagnetic Chern insulators with remarkable quantum ...anomalous Hall (QAH) properties. However, in this study, it was found that the HK Fe2O3 monolayer exhibits antiferromagnetic semiconducting properties suitable for advanced spintronics applications. Through first-principle calculations based on density functional theory (DFT) calculations, we show that the Fe2O3 monolayer has good energetic, mechanical, and dynamic stability. We further evaluate the magnetic anisotropy energies (MAE) of the Fe2O3 monolayer and find that it prefers the out-of-plane easy axis magnetization direction with a sizeable MAE value of 248.75 μeV per Fe atom. Moreover, by performing Monte Carlo (MC) simulations based on the 2D classical anisotropic Heisenberg model, we predict a Néel temperature of 631.7(5) K for the Fe2O3 monolayer. We demonstrate that the Fe2O3 monolayer belongs to the 2D Ising-like universality class based on the estimated critical exponent ratios of magnetic susceptibility, magnetization, and the exponent of the correlation length. Our findings demonstrate that the Fe2O3 monolayer can be a suitable candidate for future antiferromagnetic spintronic device applications, especially in ultra-high data processing and storage, due to the coexistence of AFM and semiconducting properties.
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•Fe2O3 monolayer has been investigated using DFT+U and Monte Carlo (MC) calculations.•The Fe2O3 monolayer exhibits robust antiferromagnetic semiconducting properties.•We predict a Néel temperature of 631.7(5) K for the Fe2O3 monolayer.•We demonstrate that the Fe2O3 monolayer belongs to the 2D Ising-like universality class.
Independence and anticonformity are two types of social behaviors known in social psychology literature and the most studied parameters in the opinion dynamics model. These parameters are responsible ...for continuous (second-order) and discontinuous (first-order) phase transition phenomena. Here, we investigate the majority rule model in which the agents adopt independence and anticonformity behaviors. We define the model on several types of graphs: complete graph, two-dimensional (2D) square lattice, and one-dimensional (1D) chain. By defining p as a probability of independence (or anticonformity), we observe the model on the complete graph undergoes a continuous phase transition where the critical points are pc≈0.334 (pc≈0.667) for the model with independent (anticonformist) agents. On the 2D square lattice, the model also undergoes a continuous phase transition with critical points at pc≈0.0608 (pc≈0.4035) for the model with independent (anticonformist) agents. On the 1D chain, there is no phase transition either with independence or anticonformity. Furthermore, with the aid of finite-size scaling analysis, we obtain the same sets of critical exponents for both models involving independent and anticonformist agents on the complete graph. Therefore they are identical to the mean-field Ising model. However, in the case of the 2D square lattice, the models with independent and anticonformist agents have different sets of critical exponents and are not identical to the 2D Ising model. Our work implies that the existence of independence behavior in a society makes it more challenging to achieve consensus compared to the same society with anticonformists.
•Analyze order-disorder phase transition phenomena based on the majority rule model.•Overview of two types of social behaviors and their impacts on critical behavior.•Identify the universality class of the model.•Impacts of two types of social behaviors on the socio-political phenomena.
The phase transition of a discrete version of the non-equilibrium Biswas–Chatterjee–Sen model, defined on Erdös–Rényi random graphs (ERRGs) and directed ERRGs random graphs (DERRGs), has been ...studied. The mutual interactions (or affinities) can be both positive and negative, depending on the noise parameter value. Through extensive Monte Carlo simulations and finite-size scaling analysis, the continuous phase transitions and the corresponding critical exponent ratios have been obtained for several values of the average connectivity z. The effective dimensionality of the system has been found to be Deff≈1.0 for all values of z, which is similar to the one obtained on Barabási–Albert networks. The present results show that kinetic models of discrete opinion dynamics belong to a different universality class as the corresponding equilibrium Ising and Potts, and non-equilibrium majority-vote models on the same ERRGs and DERRGs. It is also noticed that the kinetic model here studied on ERRGs and DERRGs is in different universality classes for connectivities z<20, while for z≥20 the critical exponents are the same for both random graphs.
We study last passage percolation in a half-quadrant, which we analyze within the framework of Pfaffian Schur processes. For the model with exponential weights, we prove that the fluctuations of the ...last passage time to a point on the diagonal are either GSE Tracy–Widom distributed, GOE Tracy–Widom distributed or Gaussian, depending on the size of weights along the diagonal. Away from the diagonal, the fluctuations of passage times follow the GUE Tracy–Widom distribution. We also obtain a two-dimensional crossover between the GUE, GOE and GSE distribution by studying the multipoint distribution of last passage times close to the diagonal when the size of the diagonal weights is simultaneously scaled close to the critical point. We expect that this crossover arises universally in KPZ growth models in half-space. Along the way, we introduce a method to deal with diverging correlation kernels of point processes where points collide in the scaling limit.
Mitra et al. (2019) proposed a new percolation model that includes distortion in the square lattice and concluded that it may belong to the same universality class as the ordinary percolation. But ...the conclusion is questionable since their results of critical exponents are not consistent. In this paper, we reexamined the new model with high precision in the square, triangular, and honeycomb lattices by using the Newman–Ziff algorithm. Through the finite-size scaling, we obtained the percolation threshold of the infinite-size lattice and critical exponents (ν and β). Our results of the critical exponents are the same as those of the classical percolation within error bars, and the percolation in distorted lattices is confirmed to belong to the universality class of the classical percolation in two dimensions.
•The percolation with distortion was reexamined with the Newman–Ziff algorithm.•The percolation was studied in distorted triangular and honeycomb lattices.•Incorrect critical exponents of percolation in a distorted square lattice were fixed.•Lattice distortion does not change the universality class of the percolation.
Modeling and investigating the properties of fundamental diagrams (FDs) in mixed traffic, which encompasses heterogeneous with non-lane-based flow, has been one of the emerging research areas in the ...past few years. The main challenges in modeling are: estimating accurate steady-state (ss) points based on empirical observations and properly representing FDs in mixed traffic conditions. The first part of this work uses the traditional discretization approach and the optimal time–space window to apply Edie’s generalized definitions to estimate the traffic flow variables and the steady states. The second part of the work involves a trajectory shear mapping method to estimate less-scattered FDs. Finally, the shape of the FDs are determined, and their properties are studied by developing area occupancy-based (ao) normalized flow and speed models. Empirical observations from multiple locations show that the power-law relationships seem to be the best fit based on the ao-based representation of the fundamental parameter that indicates the possibility of universality in the FDs from the mixed traffic conditions.
•Shear transformation of trajectories reduces scatter in fundamental diagrams.•Providing insights into Manna universality class behavior of mixed traffic.•Confirmation of location invariant power-law relationships.•Algorithm with optimal time-space steps simplifies steadystate point identification.
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