arXiv subjects

Sheng Fang

Publications and source records attributed to Sheng Fang.

35 records · Page 2Linked to original sources

arXiv2024

Finite-Size Scaling of the High-Dimensional Ising Model in the Loop Representation

Besides its original spin representation, the Ising model is known to have the Fortuin-Kasteleyn (FK) bond and loop representations, of which the former was recently shown to exhibit two upper critical dimensions $(d_c=4,d_p=6)$. Using a lifted worm algorithm, we determine the critical coupling as $K_c = 0.077\,708\,91(4)$ for $d=7$, which significantly improves over the previous results, and then study critical geometric properties of the loop-Ising clusters on tori for spatial dimensions $d=5$ to 7. We show that, as the spin representation, the loop Ising model has only one upper critical dimension at $d_c=4$. However, sophisticated finite-size scaling (FSS) behaviors, like two length scales, two configuration sectors and two scaling windows, still exist as the interplay effect of the Gaussian fixed point and complete-graph asymptotics. Moreover, using the Loop-Cluster algorithm, we provide an intuitive understanding of the emergence of the percolation-like upper critical dimension $d_p=6$ in the FK-Ising model. As a consequence, a unified physical picture is established for the FSS behaviors in all the three representations of the Ising model above $d_c=4$.

cond-mat.stat-mech↗

arXiv2023

Interplay of the complete-graph and Gaussian fixed-point asymptotics in finite-size scaling of percolation above the upper critical dimension

Percolation has two mean-field theories, the Gaussian fixed point (GFP) and the Landau mean-field theory or the complete graph (CG) asymptotics. By large-scale Monte Carlo simulations, we systematically study the interplay of the GFP and CG effects to the finite-size scaling of percolation above the upper critical dimension $d_c = 6$ with periodic, free, and cylindrical boundary conditions. Our results suggest that, with periodic boundaries, the \emph{unwrapped} correlation length scales as $L^{d/6}$ at the critical point, diverging faster than $L$ above $d_c$. As a consequence, the scaling behaviours of macroscopic quantities with respect to the linear system size $L$ follow the CG asymptotics. The distance-dependent properties, such as the short-distance behaviour of the two-point correlation function and the Fourier transformed quantities with non-zero modes, are still controlled by the GFP. With free boundaries, since the correlation length is cutoff by $L$, the finite-size scaling at the critical point is controlled by the GFP. However, some quantities are observed to exhibit the CG aysmptotics at the low-temperature pseudo-critical point, such as the sizes of the two largest clusters. With cylindrical boundaries, due to the interplay of the GFP and CG effects, the correlation length along the axial direction of the cylinder scales as $ξ_L \sim L^{(d-1)/5}$ within the critical window of size $O(L^{-2(d-1)/5})$, distinct from both periodic and free boundaries. A field-theoretical calculation for deriving the scaling of $ξ_L$ is also presented. Moreover, the one-point surface correlation function along the axial direction of the cylinder is observed to scale as $τ^{(1-d)/2}$ for short distance but then enter a plateau of order $L^{-3(d-1)/5}$ before it decays significantly fast.

cond-mat.stat-mech↗

arXiv2023

Geometric scaling behaviors of the Fortuin-Kasteleyn Ising model in high dimensions

Recently, we argued [Chin. Phys. Lett. $39$, 080502 (2022)] that the Ising model simultaneously exhibits two upper critical dimensions $(d_c=4, d_p=6)$ in the Fortuin-Kasteleyn (FK) random-cluster representation. In this paper, we perform a systematic study of the FK Ising model on hypercubic lattices with spatial dimensions $d$ from 5 to 7, and on the complete graph. We provide a detailed data analysis of the critical behaviors of a variety of quantities at and near the critical points. Our results clearly show that many quantities exhibit distinct critical phenomena for $4 < d < 6$ and $d\geq 6$, and thus strongly support the argument that $6$ is also an upper critical dimension. Moreover, for each studied dimension, we observe the existence of two configuration sectors, two lengthscales, as well as two scaling windows, and thus, two sets of critical exponents are needed to describe these behaviors. Our finding enriches the understanding of the critical phenomena in the Ising model.

cond-mat.stat-mech↗

arXiv2023

Geometric properties of the complete-graph Ising model in the loop representation

The exact solution of the Ising model on the complete graph (CG) provides an important, though mean-field, insight for the theory of continuous phase transitions. Besides the original spin, the Ising model can be formulated in the Fortuin-Kasteleyn random-cluster and the loop representation, in which many geometric quantities have no correspondence in the spin representations. Using a lifted-worm irreversible algorithm, we study the CG-Ising model in the loop representation, and, based on theoretical and numerical analyses, obtain a number of exact results including volume fractal dimensions and scaling forms. Moreover, by combining with the Loop-Cluster algorithm, we demonstrate how the loop representation can provide an intuitive understanding to the recently observed rich geometric phenomena in the random-cluster representation, including the emergence of two configuration sectors, two length scales and two scaling windows.

cond-mat.stat-mech↗

arXiv2022

Changer: Feature Interaction is What You Need for Change Detection

Change detection is an important tool for long-term earth observation missions. It takes bi-temporal images as input and predicts "where" the change has occurred. Different from other dense prediction tasks, a meaningful consideration for change detection is the interaction between bi-temporal features. With this motivation, in this paper we propose a novel general change detection architecture, MetaChanger, which includes a series of alternative interaction layers in the feature extractor. To verify the effectiveness of MetaChanger, we propose two derived models, ChangerAD and ChangerEx with simple interaction strategies: Aggregation-Distribution (AD) and "exchange". AD is abstracted from some complex interaction methods, and "exchange" is a completely parameter\&computation-free operation by exchanging bi-temporal features. In addition, for better alignment of bi-temporal features, we propose a flow dual-alignment fusion (FDAF) module which allows interactive alignment and feature fusion. Crucially, we observe Changer series models achieve competitive performance on different scale change detection datasets. Further, our proposed ChangerAD and ChangerEx could serve as a starting baseline for future MetaChanger design.

cs.CV↗

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

Fluid laminarization in protein-based high internal phase emulsions process

Protein-based high internal phase emulsions (HIPEs) have gained tremendous attention in diverse fields, but their mechanism in the emulsification process remains elusive. In this article, HIPEs were stabilized directly by food-grade proteins, depending on a self-organized process featuring a fluid laminarization. We elucidated that the emulsification with the rotor-stator mixer is a typical non-equilibrium process. The crucial factor for the process is related to the irreversible energy dissipation, while the internal phase volume fraction is the threshold determining the laminarization. The feasible explanation speculated that the transition corresponds to the dissipative structure, i.e., compressive droplets, arising from the spatiotemporal self-organization, to dissipate the turbulent kinetic energy. We found a new paradigm of dissipative structure, comprehending such structure in the HIPEs emulsification process, which is expected to pave the way for its industrial-scale production with the virtue of low-cost proteins.

cond-mat.soft↗

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↗

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

Salient Positions based Attention Network for Image Classification

The self-attention mechanism has attracted wide publicity for its most important advantage of modeling long dependency, and its variations in computer vision tasks, the non-local block tries to model the global dependency of the input feature maps. Gathering global contextual information will inevitably need a tremendous amount of memory and computing resources, which has been extensively studied in the past several years. However, there is a further problem with the self-attention scheme: is all information gathered from the global scope helpful for the contextual modelling? To our knowledge, few studies have focused on the problem. Aimed at both questions this paper proposes the salient positions-based attention scheme SPANet, which is inspired by some interesting observations on the attention maps and affinity matrices generated in self-attention scheme. We believe these observations are beneficial for better understanding of the self-attention. SPANet uses the salient positions selection algorithm to select only a limited amount of salient points to attend in the attention map computing. This approach will not only spare a lot of memory and computing resources, but also try to distill the positive information from the transformation of the input feature maps. In the implementation, considering the feature maps with channel high dimensions, which are completely different from the general visual image, we take the squared power of the feature maps along the channel dimension as the saliency metric of the positions. In general, different from the non-local block method, SPANet models the contextual information using only the selected positions instead of all, along the channel dimension instead of space dimension. Our source code is available at https://github.com/likyoo/SPANet.

cs.CV↗

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

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↗

arXiv2020

Complete graph and Gaussian fixed point asymptotics in the five-dimensional Fortuin-Kasteleyn Ising model with periodic boundaries

We present an extensive Markov-chain Monte Carlo study of the finite-size scaling behavior of the Fortuin-Kasteleyn Ising model on five-dimensional hypercubic lattices with periodic boundary conditions. We observe that physical quantities, which include the contribution of the largest cluster, exhibit complete graph asymptotics. However, for quantities, where the contribution of the largest cluster is removed, we observe that the scaling behavior is mainly controlled by the Gaussian fixed point. Our results therefore suggest that \textit{both} scaling predictions, i.e. the complete graph \textit{and} the Gaussian fixed point asymptotics, are needed to provide a complete description for the five-dimensional finite-size scaling behavior on the torus.

cond-mat.stat-mech↗

arXiv2020

Critical exponents and universal excess cluster number of percolation in four and five dimensions

We study critical bond percolation on periodic four-dimensional (4D) and five-dimensional (5D) hypercubes by Monte Carlo simulations. By classifying the occupied bonds into branches, junctions and non-bridges, we construct the whole, the leaf-free and the bridge-free clusters using the breadth-first-search algorithm. From the geometric properties of these clusters, we determine a set of four critical exponents, including the thermal exponent $y_{\rm t} \equiv 1/ν$, the fractal dimension $d_{\rm f}$, the backbone exponent $d_{\rm B}$ and the shortest-path exponent $d_{\rm min}$. We also obtain an estimate of the excess cluster number $b$ which is a universal quantity related to the finite-size scaling of the total number of clusters. The results are $y_{\rm t} = 1.461(5)$, $d_{\rm f} = 3.044 \, 6(7)$, $d_{\rm B} = 1.984\,4(11)$, $d_{\rm min} = 1.604 \, 2(5)$, $b = 0.62(1)$ for 4D; and $y_{\rm t} = 1.743(10)$, $d_{\rm f} = 3.526\,0(14)$, $d_{\rm B} = 2.022\,6(27)$, $d_{\rm min} = 1.813\, 7(16)$, $b = 0.62(2)$ for 5D. The values of the critical exponents are compatible with or improving over the existing estimates, and those of the excess cluster number $b$ have not been reported before. Together with the existing values in other spatial dimensions $d$, the $d$-dependent behavior of the critical exponents is obtained, and a local maximum of $d_{\rm B}$ is observed near $d \approx 5$. It is suggested that, as expected, critical percolation clusters become more and more dendritic as $d$ increases.

cond-mat.stat-mech↗

arXiv2018

Geometric properties of the Fortuin-Kasteleyn representation of the Ising model

We present a Monte Carlo study of the Fortuin-Kasteleyn (FK) clusters of the Ising model on the square (2D) and simple-cubic (3D) lattices. The wrapping probability, a dimensionless quantity characterizing the topology of the FK clusters on a torus, is found to suffer from smaller finite-size corrections than the well-known Binder ratio, and yields a high-precision critical coupling as $K_c(3\rm D)=0.221\,654\,631(8)$. We then study geometric properties of the FK clusters at criticality. It is demonstrated that the distribution of the critical largest-cluster size $C_1$ follows a single-variable function as $P(C_1,L){\rm d}C_1=\tilde P(x){\rm d}x$ with $x\equiv C_1/L^{d_{\rm F}}$ ($L$ is the linear size), and that the fractal dimension $d_{\rm F}$ is identical to the magnetic exponent. An interesting bimodal feature is observed in distribution $\tilde P(x)$ in 3D, and attributed to the different approaching behaviors for $K \to K_c+0^\pm$. For a critical FK configuration, the cluster number per site $n(s,L)$ of size $s$ is confirmed to obey the standard scaling form $n(s,L)\sim s^{-τ}\tilde n(s/L^{d_{\rm F}})$, with hyper-scaling relation $τ=1+d/d_{\rm F}$ and the spatial dimension $d$. To further characterize the compactness of the FK clusters, we measure their graph distances and determine the shortest-path exponents as $d_{\rm min}(3\rm D)=1.259\,4(2)$ and $d_{\rm min}(2\rm D)=1.094\,0(3)$. Further, by excluding all the bridges from the occupied bonds, we obtain bridge-free configurations and determine the backbone exponents as $d_{\rm B}(3\rm D)=2.167\,3(15)$ and $d_{\rm B}(2\rm D)=1.732\,1(4)$. The estimates of the universal wrapping probabilities for the 3D Ising model and of the geometric critical exponents $d_{\rm min}$ and $d_{\rm B}$ either improve over the existing results or have not been reported yet.

cond-mat.stat-mech↗

arXiv2018

Random-length Random Walks and Finite-size scaling in high dimensions

We address a long-standing debate regarding the finite-size scaling of the Ising model in high dimensions, by introducing a random-length random walk model, which we then study rigorously. We prove that this model exhibits the same universal FSS behaviour previously conjectured for the self-avoiding walk and Ising model on finite boxes in high-dimensional lattices. Our results show that the mean walk length of the random walk model controls the scaling behaviour of the corresponding Green's function. We numerically demonstrate the universality of our rigorous findings by extensive Monte Carlo simulations of the Ising model and self-avoiding walk on five-dimensional hypercubic lattices with free and periodic boundaries.

cond-mat.stat-mech↗