arXiv subjects

Youjin Deng

Publications and source records attributed to Youjin Deng.

At least 109 records · Page 6Linked to original sources

arXiv2022

Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems

We combine percolation theory and Monte Carlo simulation to study in two dimensions the connectivity of an equilibrium lattice model of interacting Janus disks which self-assemble into an orientationally ordered stripe phase at low temperature. As the patch size is increased or the temperature is lowered, clusters of patch-connected disks grow, and a percolating cluster emerges at a threshold. In the stripe phase, the critical clusters extend longer in the direction parallel to the stripes than in the perpendicular direction, and percolation is thus anisotropic. It is found that the critical behavior of percolation in the Janus system is consistent with that of standard isotropic percolation, when an appropriate spatial rescaling is made. The rescaling procedure can be applied to understand other anisotropic systems, such as the percolation of aligned rigid rods and of the $q$-state Potts model with anisotropic interactions.

cond-mat.soft↗

arXiv2022

Burstiness and information spreading in the active particles systems

We construct the temporal network using the two-dimensional active particle systems which are described by the Vicsek model. The bursts of the interevent times for a specific pair of particles are investigated numerically. We find that for different noise strength, the distribution of the interevent times of a target edge follows by a heavy-tail, revealing a strong burstiness of the signals. To further characterize the nature of the burstiness, the burstiness parameter and the memory coefficient are calculated. The results show that near the critical points of the Vicsek model, the burstiness parameters reach the minimum values for each density, indicating a relation between the phase transition of the Vicsek model and the bursty nature of the signals. Besides, the memory plays a negligible role in the burstiness. Further, we investigate the spreading dynamics on our temporal network with the susceptible-infected model, and observe a positive correlation between the burstiness and the information spreading dynamics.

cond-mat.stat-mech↗

arXiv2022

Exchange-correlation effect in the charge response of a warm dense electron gas

The study of warm dense matter, widely existing in nature and laboratories, is challenging due to the interplay of quantum and classical fluctuations. We develop a variational diagrammatic Monte Carlo method and determine the exchange-correlation kernel $K_{\rm XC}(q;T)$ of a warm dense electron gas for a broad range of temperature $T$ and momentum $q$. We observe several interesting physics, including the $T$-dependent evolution of the hump structure and the large-$q$ tail and the emergence of a scaling relation. Particularly, by deriving an analytical form for $q \to \infty$, we obtain large-$q$ tails of $K_{\rm XC}$ with high precision. It is shown that the $K_{\rm XC}$ data can be reliably transformed into real space, which can be directly used in density-functional-theory calculations of real warm dense matter.

physics.plasm-ph↗

arXiv2022

Geometric Upper Critical Dimensions of the Ising Model

The upper critical dimension of the Ising model is known to be $d_c=4$, above which critical behavior is regarded as trivial. We hereby argue from extensive simulations that, in the random-cluster representation, the Ising model simultaneously exhibits two upper critical dimensions at $(d_c= 4, d_p=6)$, and critical clusters for $d \geq d_p$, except the largest one, are governed by exponents from percolation universality. We predict a rich variety of geometric properties and then provide strong evidence in dimensions from 4 to 7 and on complete graphs. Our findings significantly advance the understanding of the Ising model, which is a fundamental system in many branches of physics.

cond-mat.stat-mech↗

arXiv2022

Monte Carlo study of duality and the Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional $q$-state clock model in flow representations

The two-dimensional $q$-state clock model for $q \geq 5$ undergoes two Berezinskii-Kosterlitz-Thouless (BKT) phase transitions as temperature decreases. Here we report an extensive worm-type simulation of the square-lattice clock model for $q=$5--9 in a pair of flow representations, from the high- and low-temperature expansions, respectively. By finite-size scaling analysis of susceptibility-like quantities, we determine the critical points with a precision improving over the existing results. Due to the dual flow representations, each point in the critical region is observed to simultaneously exhibit a pair of anomalous dimensions, which are $η_1=1/4$ and $η_2 = 4/q^2$ at the two BKT transitions. Further, the approximate self-dual points $β_{\rm sd}(L)$, defined by the stringent condition that the susceptibility like quantities in both flow representations are identical, are found to be nearly independent of system size $L$ and behave as $β_{\rm sd} \simeq q/2π$ asymptotically at the large-$q$ limit. The exponent $η$ at $β_{\rm sd}$ is consistent with $1/q$ within statistical error as long as $q \geq 5$. Based on this, we further conjecture that $η(β_{\rm sd}) = 1/q$ holds exactly and is universal for systems in the $q$-state clock universality class. Our work provides a vivid demonstration of rich phenomena associated with the duality and self-duality of the clock model in two dimensions.

cond-mat.stat-mech↗

arXiv2022

Multiple and Asymmetric Scalings in Explosive Percolation

Explosive percolation in the Achlioptas process has recently attracted much research attention. From extensive simulations in an event-based ensemble, we find that, in dimensions from $2$ to $6$ and on random graphs, the Achlioptas processes all have two scaling windows and multiple fractal structures. The mixing of these multiple scalings successfully explains the previously observed anomalous phenomena in the conventional ensemble, and, moreover, correct critical exponents are now determined with a high precision by the event-based method. The multiple scalings and the ensemble inequivalence may bring new insights for other statistical systems.

cond-mat.stat-mech↗

arXiv2022

Surface criticality of antiferromagnetic Potts model

We study the three-state antiferromagnetic Potts model on the simple-cubic lattice, paying attention to the surface critical behaviors. When the nearest neighboring interactions of the surface is tuned, we obtain a phase diagram similar to the XY model, owing to the emergent O(2) symmetry of the bulk critical point. For the ordinary transition, we get $y_{h1}=0.780(3)$, $η_\parallel=1.44(1)$, and $η_\perp=0.736(6)$; for the special transition, we get $y_s=0.59(1)$, $y_{h1}=1.693(2)$, $η_\parallel=-0.391(4)$, and $η_\perp=-0.179(5)$; in the extraordinary-log phase, the surface correlation function $C_\parallel(r)$ decays logarithmically, with decaying exponent $q=0.60(2)$, however, the correlation $C_\perp(r)$ still decays algebraically, with critical exponent $η_\perp=-0.442(5)$. If the ferromagnetic next nearest neighboring surface interactions are added, we find two transition points, the first one is a special point between the ordinary phase and the extraordinary-log phase, the second one is a transition between the extraordinary-log phase and the $Z_6$ symmetry-breaking phase, with critical exponent $y_{\rm s}=0.41(2)$. The scaling behaviors of the second transition is very interesting, the surface spin correlation function $C_\parallel(r)$ and the surface squared staggered magnetization at this point decays logarithmically, with exponent $q=0.37(1)$; however, the surface structure factor with the smallest wave vector and the correlation function $C_\perp(r)$ satisfy power-law decaying, with critical exponents $η_\parallel=-0.69(1)$ and $η_\perp=-0.37(1)$, respectively.

cond-mat.stat-mech↗

arXiv2022

Backbone and shortest-path exponents of the two-dimensional $Q$-state Potts model

We present a Monte Carlo study of the backbone and the shortest-path exponents of the two-dimensional $Q$-state Potts model in the Fortuin-Kasteleyn bond representation. We first use cluster algorithms to simulate the critical Potts model on the square lattice and obtain the backbone exponents $d_{\rm B} = 1.732 \, 0(3)$ and $1.794(2)$ for $Q=2,3$ respectively. However, for large $Q$, the study suffers from serious critical slowing down and slowly converging finite-size corrections. To overcome these difficulties, we consider the O$(n)$ loop model on the honeycomb lattice in the densely packed phase, which is regarded to correspond to the critical Potts model with $Q=n^2$. With a highly efficient cluster algorithm, we determine from domains enclosed by the loops $d_{\rm B} =1.643\,39(5), 1.732\,27(8), 1.793\,8(3), 1.838\,4(5), 1.875\,3(6)$ for $Q = 1, 2, 3, 2 \! + \! \sqrt{3}, 4$, respectively, and $d_{\rm min} = 1.094\,5(2), 1.067\,5(3), 1.047\,5(3), 1.032\,2(4)$ for $Q=2,3, 2+\sqrt{3}, 4$ respectively. Our estimates significantly improve over the existing results for both $d_{\rm B}$ and $d_{\rm min}$. Finally, by studying finite-size corrections in backbone-related quantities, we conjecture an exact formula as a function of $n$ for the leading correction exponent.

cond-mat.stat-mech↗

arXiv2022

Unwrapped two-point functions on high-dimensional tori

We study unwrapped two-point functions for the Ising model, the self-avoiding walk and a random-length loop-erased random walk on high-dimensional lattices with periodic boundary conditions. While the standard two-point functions of these models have been observed to display an anomalous plateau behaviour, the unwrapped two-point functions are shown to display standard mean-field behaviour. Moreover, we argue that the asymptotic behaviour of these unwrapped two-point functions on the torus can be understood in terms of the standard two-point function of a random-length random walk model on Zd. A precise description is derived for the asymptotic behaviour of the latter. Finally, we consider a natural notion of the Ising walk length, and show numerically that the Ising and SAW walk lengths on high-dimensional tori show the same universal behaviour known for the SAW walk length on the complete graph.

math-ph↗

arXiv2022

Machine learning for percolation utilizing auxiliary Ising variables

Machine learning for phase transition has received intensive research interest in recent years. However, its application in percolation still remains challenging. We propose an auxiliary Ising mapping method for machine learning study of the standard percolation as well as a variety of statistical mechanical systems in correlated percolation representations. We demonstrate that unsupervised machine learning is able to accurately locate the percolation threshold, independent of the spatial dimension of system or the type of phase transition, which can be first order or continuous. Moreover, we show that, by neural network machine learning, auxiliary Ising configurations for different universalities can be classified with high confidence level. Our results indicate that the auxiliary Ising mapping method, despite of it simplicity, can advance the application of machine learning in statistical and condensed-matter physics.

cond-mat.stat-mech↗

arXiv2021

Dynamic formation of quasicondensate and spontaneous vortices in a strongly interacting Fermi gas

We report an experimental study of quench dynamics across the superfluid transition temperature $T_c$ in a strongly interacting Fermi gas by ramping down the trapping potential. The nonzero quasi-condensate number $N_0$ at temperature significantly above $T_c$ in the unitary and the BEC regimes reveals the pseudogap physics. Below $T_c$, a rapid growth of $N_0$ is accompanied by spontaneous generation of tens of vortices. We observe a power law scaling of the vortex density versus the quasi-condensate formation time, consistent with the Kibble-Zurek theory. Our work provides an example of studying emerged many-body physics by quench dynamics and paves the way for studying the quantum turbulence in a strongly interacting Fermi gas.

cond-mat.quant-gas↗

arXiv2021

Logarithmic finite-size scaling of the self-avoiding walk at four dimensions

The $n$-vector spin model, which includes the self-avoiding walk (SAW) as a special case for the $n \rightarrow 0 $ limit, has an upper critical dimensionality at four spatial dimensions (4D). We simulate the SAW on 4D hypercubic lattices with periodic boundary conditions by an irreversible Berretti-Sokal algorithm up to linear size $L=768$. From an unwrapped end-to-end distance, we obtain the critical fugacity as $z_c= 0.147 \, 622 \, 380(2)$, improving over the existing result $z_c=0.147 \, 622 \, 3(1)$ by 50 times. Such a precisely estimated critical point enables us to perform a systematic study of the finite-size scaling of 4D SAW for various quantities. Our data indicate that near $z_c$, the scaling behavior of the free energy simultaneously contains a scaling term from the Gaussian fixed point and the other accounting for multiplicative logarithmic corrections. In particular, it is clearly observed that the critical magnetic susceptibility and the specific heat logarithmically diverge as $χ\sim L^2 (\ln L)^{2 \hat{y}_h}$ and $C \sim (\ln L)^{2 \hat{y}_t}$, and the logarithmic exponents are determined as $\hat{y}_h=0.252(2)$ and $\hat{y}_t=0.25(2)$, in excellent agreement with the field theoretical prediction $\hat{y}_h=\hat{y}_t=1/4$. Our results provide a strong support for the recently conjectured finite-size scaling form for the O$(n)$ universality classes at 4D.

cond-mat.stat-mech↗

arXiv2021

Topological Higgs Amplitude Modes in Strongly Interacting Superfluids

By studying the 2-dimensional Su-Schrieffer-Heeger-Bose-Hubbard model, we show the existence of topological Higgs amplitude modes in the strongly interacting superfluid phase. Using the slave boson approach, we find that, in the large filling limit, the Higgs excitations and the Goldstone excitations above the ground state are well decoupled, and both of them exhibit nontrivial topology inherited from the underlying noninteracting bands. At finite fillings, they become coupled at high energies; nevertheless, the topology of these modes are unchanged. Moreover, based on an effective action analysis, we further provide a universal physical picture for the topological character of Higgs and Goldstone modes. Our discovery of the first realization of the topological Higgs mode opens the path to novel investigations in various systems such as superconductors and quantum magnetism.

cond-mat.quant-gas↗

arXiv2021

Extraordinary-log surface phase transition in the three-dimensional $XY$ model

Universality is a pillar of modern critical phenomena. The standard scenario is that the two-point correlation algebraically decreases with the distance $r$ as $g(r) \sim r^{2-d-η}$, with $d$ the spatial dimension and $η$ the anomalous dimension. Very recently, a logarithmic universality was proposed to describe the extraordinary surface transition of O($N$) system. In this logarithmic universality, $g(r)$ decays in a power of logarithmic distance as $g(r) \sim ({\rm ln}r)^{-\hatη}$, dramatically different from the standard scenario. We explore the three-dimensional $XY$ model by Monte Carlo simulations, and provide strong evidence for the emergence of logarithmic universality. Moreover, we propose that the finite-size scaling of $g(r,L)$ has a two-distance behavior: simultaneously containing a large-distance plateau whose height decays logarithmically with $L$ as $g(L) \sim ({\rm ln}L)^{-\hatη'}$ as well as the $r$-dependent term $g(r) \sim ({\rm ln}r)^{-\hatη}$, with ${\hatη'} \approx {\hatη}-1$. The critical exponent $\hatη'$, characterizing the height of the plateau, obeys the scaling relation $\hatη'=(N-1)/(2πα)$ with the RG parameter $α$ of helicity modulus. Our picture can also explain the recent numerical results of a Heisenberg system. The advances on logarithmic universality significantly expand our understanding of critical universality.

cond-mat.stat-mech↗

arXiv2021

Superfluid ground state phase diagram of the two-dimensional Hubbard model in the emergent Bardeen-Cooper-Schrieffer regime

In nonperturbative regimes, the superfluid instability in the two-dimensional Hubbard model can be described by an emergent BCS theory with small effective pairing constants. We compute the effective couplings using a controlled bold-line diagrammatic Monte Carlo approach, which stochastically sums all skeleton Feynman diagrams dressed in the one- and two-particle channels to high expansion orders, and map out the resulting superfluid ground-state phase diagram in a range of next-nearest-neighbor hopping $0 \leq t^{\prime} \leq 0.3t$, interaction strength $0 \leq U \leq 3t$, and lattice filling $0 \leq n \leq 2$. The phase diagram is dramatically transformed in the hole-doped region and becomes particularly rich at larger doping and $t'$. At $t'=0.3$, the weak-coupling picture with the dominant triplet pairing sharply peaked at $n \approx 0.73$ due to the Van Hove singularity is replaced by a plateau of the singlet $d_{x^2-y^2}$ paring, while for $U \gtrsim 3t$ the effective couplings are consistent with the $d_{x^2-y^2}$ high-temperature superconductivity in the hole-doped region near cuprates' optimal doping.

cond-mat.str-el↗

arXiv2021

Percolation effects in the Fortuin-Kasteleyn Ising model on the complete graph

The Fortuin-Kasteleyn (FK) random cluster model, which can be exactly mapped from the $q$-state Potts spin model, is a correlated bond percolation model. By extensive Monte Carlo simulations, we study the FK bond representation of the critical Ising model ($q=2$) on a finite complete graph, i.e. the mean-field Ising model. We provide strong numerical evidence that the configuration space for $q=2$ contains an asymptotically vanishing sector in which quantities exhibit the same finite-size scaling as in the critical uncorrelated bond percolation ($q=1$) on the complete graph. Moreover, we observe that in the full configuration space, the power-law behaviour of the cluster-size distribution for the FK Ising clusters except the largest one is governed by a Fisher exponent taking the value for $q=1$ instead of $q=2$. This demonstrates the percolation effects in the FK Ising model on the complete graph.

cond-mat.stat-mech↗

arXiv2021

Nested Closed Paths in Two-Dimensional Percolation

For two-dimensional percolation on a domain with the topology of a disc, we introduce a nested-path operator (NP) and thus a continuous family of one-point functions $W_k \equiv \langle \mathcal{R} \cdot k^\ell \rangle $, where $\ell$ is the number of independent nested closed paths surrounding the center, $k$ is a path fugacity, and $\mathcal{R}$ projects on configurations having a cluster connecting the center to the boundary. At criticality, we observe a power-law scaling $W_k \sim L^{X_{\rm NP}}$, with $L$ the linear system size, and we determine the exponent $X_{\rm NP}$ as a function of $k$. On the basis of our numerical results, we conjecture an analytical formula, $X_{\rm NP} (k) = \frac{3}{4}ϕ^2 -\frac{5}{48}ϕ^2/ (ϕ^2-\frac{2}{3})$ where $k = 2 \cos(πϕ)$, which reproduces the exact results for $k=0,1$ and agrees with the high-precision estimate of $X_{\rm NP}$ for other $k$ values. In addition, we observe that $W_2(L)=1$ for site percolation on the triangular lattice with any size $L$, and we prove this identity for all self-matching lattices.

cond-mat.stat-mech↗

arXiv2021

Two-scale scenario of rigidity percolation of sticky particles

In the presence of attraction, the jamming transition of packings of frictionless particles corresponds to the rigidity percolation. When the range of attraction is long, the distribution of the size of rigid clusters, $P(s)$, is continuous and shows a power-law decay. For systems with short-range attractions, however, $P(s)$ appears discontinuous. There is a power-law decay for small cluster sizes, followed by a low probability gap and a peak near the system size. We find that this appearing ``discontinuity'' does not mean that the transition is discontinuous. In fact, it signifies the coexistence of two distinct length scales, associated with the largest cluster and smaller ones, respectively. The comparison between the largest and second largest clusters indicates that their growth rates with system size are rather different. However, both cluster sizes tend to diverge in the large system size limit, suggesting that the jamming transition of systems with short-range attractions is still continuous. In the framework of the two-scale scenario, we also derive a generalized hyperscaling relation. With robust evidence, our work challenges the former single-scale view of the rigidity percolation.

cond-mat.soft↗