Extraordinary-log Universality of Critical Phenomena in Plane Defects.

The recent discovery of the extraordinary-log (E-Log) criticality is a celebrated achievement in modern critical theory and calls for generalization. Using large-scale Monte Carlo simulations, we study the critical phenomena of plane defects in three- and four-dimensional O(n) critical systems. In three dimensions, we provide the first numerical proof for the E-Log criticality of plane defects. In particular, for n=2, the critical exponent q[over ^] of two-point correlation and the renormalization-group parameter α of helicity modulus conform to the scaling relation q[over ^]=(n-1)/(2πα), whereas the results for n≥3 violate this scaling relation. In four dimensions, it is strikingly found that the E-Log criticality also emerges in the plane defect. These findings have numerous potential realizations and would boost the ongoing advancement of conformal field theory.

Finite-size scaling of O(n) systems at the upper critical dimensionality.

Logarithmic finite-size scaling of the O(n) universality class at the upper critical dimensionality (d c = 4) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems. Here, we address this long-standing problem in the context of the n-vector model (n = 1, 2, 3) on periodic four-dimensional hypercubic lattices. We establish an explicit scaling form for the free-energy density, which simultaneously consists of a scaling term for the Gaussian fixed point and another term with multiplicative logarithmic corrections. In particular, we conjecture that the critical two-point correlation g(r, L), with L the linear size, exhibits a two-length behavior: follows [Formula: see text] governed by the Gaussian fixed point at shorter distances and enters a plateau at larger distances whose height decays as [Formula: see text] with [Formula: see text] a logarithmic correction exponent. Using extensive Monte Carlo simulations, we provide complementary evidence for the predictions through the finite-size scaling of observables, including the two-point correlation, the magnetic fluctuations at zero and nonzero Fourier modes and the Binder cumulant. Our work sheds light on the formulation of logarithmic finite-size scaling and has practical applications in experimental systems.

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)∼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 the O(N) system. In this logarithmic universality, g(r) decays in a power of logarithmic distance as g(r)∼(lnr)^{-η[over ^]}, 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)∼(lnL)^{-η[over ^]^{'}} as well as the r-dependent term g(r)∼(lnr)^{-η[over ^]}, with η[over ^]^{'}≈η[over ^]-1. The critical exponent η[over ^]^{'}, characterizing the height of the plateau, obeys the scaling relation η[over ^]^{'}=(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.

History-dependent percolation in two dimensions.

We study the history-dependent percolation in two dimensions, which evolves in generations from standard bond-percolation configurations through iteratively removing occupied bonds. Extensive simulations are performed for various generations on periodic square lattices up to side length L=4096. From finite-size scaling, we find that the model undergoes a continuous phase transition, which, for any finite number of generations, falls into the universality of standard two-dimensional (2D) percolation. At the limit of infinite generation, we determine the correlation-length exponent 1/ν=0.828(5) and the fractal dimension d_{f}=1.8644(7), which are not equal to 1/ν=3/4 and d_{f}=91/48 for 2D percolation. Hence, the transition in the infinite-generation limit falls outside the standard percolation universality and differs from the discontinuous transition of history-dependent percolation on random networks. Further, a crossover phenomenon is observed between the two universalities in infinite and finite generations.

Unique Landau-level structure of monolayer black phosphorus under an exponentially decaying magnetic field.

We study the Landau-level spectrum of a monolayer black phosphorus under an exponentially decaying magnetic field along one spatial dimension. The results show that unlike the case in a constant magnetic field, the number of Landau levels in the inhomogeneous magnetic field is finite, and the Landau-level structure of the system is strongly dependent on the inhomogeneity of the magnetic field. In particular, the crossing of some Landau levels apparently occurs, and the accidental degeneracy points between the levels for the conduction and valence bands are highly anisotropic due to the anisotropic effective masses in monolayer black phosphorus. The above unique characteristics of the Landau-level structure in an exponentially decaying magnetic field could be directly confirmed by the magneto-absorption and transport measurements.

Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations.

We provide a criterion based on graph duality to predict whether the three-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge c=1. The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the three-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.

Coulomb Liquid Phases of Bosonic Cluster Mott Insulators on a Pyrochlore Lattice.

Employing large-scale quantum Monte Carlo simulations, we reveal the full phase diagram of the extended Hubbard model of hard-core bosons on the pyrochlore lattice with partial fillings. When the intersite repulsion is dominant, the system is in a cluster Mott insulator phase with an integer number of bosons localized inside the tetrahedral units of the pyrochlore lattice. We show that the full phase diagram contains three cluster Mott insulator phases with 1/4, 1/2, and 3/4 boson fillings, respectively. We further demonstrate that all three cluster Mott insulators are Coulomb liquid phases and its low-energy property is described by the emergent compact U(1) quantum electrodynamics. In addition to measuring the specific heat and entropy of the cluster Mott insulators, we investigate the correlation function of the emergent electric field and verify it is consistent with the compact U(1) quantum electrodynamics description. Our result sheds light on the magnetic properties of various pyrochlore systems, as well as the charge physics of the cluster magnets.

[Measurement of myeloid-derived suppressor cells and T-helper 17 cells in peripheral blood of young children with recurrent wheezing].

OBJECTIVE: To determine the frequencies and significance of myeloid-derived suppressor cells (MDSCs) and T-helper 17 (Th17) cells in peripheral blood of young children with recurrent wheezing. METHODS: Thirty young children with an acute exacerbation of recurrent wheezing were randomly enrolled. Twenty age-matched children with bronchopneumonia (pneumonia group) and 23 age-matched preoperative children with non-infectious or non-neoplastic diseases (hernia or renal calculus) (control group) were selected. The frequencies of MDSCs and Th17 cells in the peripheral blood were measured using flow cytometry and their correlation was determined by the Spearman's correlation coefficient. RESULTS: The percentage of MDSCs in nucleated cells was significantly higher in the wheezing group than in the pneumonia and control groups (P<0.05), and it was significantly higher in the pneumonia group than in the control group (P<0.05). The percentage of Th17 cells in mononuclear cells was significantly higher in the wheezing group than in the pneumonia and control groups (P<0.05), but it showed no significant difference between the pneumonia and control groups (P>0.05). The frequency of MDSCs was positively correlated with the frequency of Th17 cells in the wheezing group (r=0.645, P<0.01). CONCLUSIONS: MDSCs and Th17 cells may contribute to the pathogenesis of recurrent wheezing in young children.

Scaling of cluster heterogeneity in the two-dimensional Potts model.

Cluster heterogeneity, the number of clusters of mutually distinct sizes, has been recently studied for explosive percolation and standard percolation [H. K. Lee et al., Phys. Rev. E 84, 020101(R) (2011); J. D. Noh et al., Phys. Rev. E 84, 010101(R) (2011)]. In this work we study the scaling of various quantities related with cluster heterogeneity in a broader context of two-dimensional q-state Potts model. We predict, via an analytic approach, the critical exponents for most of the measured quantities, and confirm these predications for various q values using extensive Monte Carlo simulations.

Testing a model with an extended O(2) symmetry in two and three dimensions.

We investigate a model with an extended O(2) symmetry in two and three dimensions, using the combination of extensive Monte Carlo simulations and the finite-size scaling. On this basis, we establish rich phase diagrams, which are constituted by O(2) critical lines. From various prospectives, the ordered states on the phase diagrams can be classified into intraspecies and interspecies correlated phases, quasi-long-range and long-range ordered phases, or ferromagnetic and antiferromagnetic phases. We furthermore show that the dimensionality effect acts on not only the ordering property, but also the topological structure of the phase diagram.

Worm-type Monte Carlo simulation of the Ashkin-Teller model on the triangular lattice.

We investigate the symmetric Ashkin-Teller (AT) model on the triangular lattice in the antiferromagnetic two-spin coupling region (J<0). In the J→-∞ limit, we map the AT model onto a fully packed loop-dimer model on the honeycomb lattice. On the basis of this exact transformation and the low-temperature expansion, we formulate a variant of worm-type algorithms for the AT model, which significantly suppress the critical slowing down. We analyze the Monte Carlo data by finite-size scaling, and locate a line of critical points of the Ising universality class in the region J<0 and K>0, with K the four-spin interaction. Further, we find that, in the J→-∞ limit, the critical line terminates at the decoupled point K=0. From the numerical results and the exact mapping, we conjecture that this "tricritical" point (J→-∞,K=0) is Berezinsky-Kosterlitz-Thouless-like and the logarithmic correction is absent. The dynamic critical exponent of the worm algorithm is estimated as z=0.28(1) near (J→-∞,K=0).