arXiv subjects

Wenan Guo

Publications and source records attributed to Wenan Guo.

At least 73 records · Page 4Linked to original sources

arXiv2013

Ising-like phase transition of an n-component Eulerian face-cubic model

By means of Monte Carlo simulations and a finite-size scaling analysis, we find a critical line of an n-component Eulerian face-cubic model on the square lattice and the simple cubic lattice in the region v>1, where v is the bond weight. The phase transition belongs to the Ising universality class independent of n. The critical properties of the phase transition can also be captured by the percolation of the complement of the Eulerian graph.

cond-mat.stat-mech↗

arXiv2013

Accurate expansions of internal energy and specific heat of critical two-dimensional Ising model with free boundaries

The bond-propagation (BP) algorithm for the specific heat of the two dimensional Ising model is developed and that for the internal energy is completed. Using these algorithms, we study the critical internal energy and specific heat of the model on the square lattice and triangular lattice with free boundaries. Comparing with previous works [X.-T. Wu {\it et al} Phys. Rev. E {\bf 86}, 041149 (2012) and Phys. Rev. E {\bf 87}, 022124 (2013)], we reach much higher accuracy ($10^{-26}$) of the internal energy and specific heat, compared to the accuracy $10^{-11}$ of the internal energy and $10^{-9}$ of the specific heat reached in the previous works. This leads to much more accurate estimations of the edge and corner terms. The exact values of some edge and corner terms are therefore conjectured. The accurate forms of finite-size scaling for the internal energy and specific heat are determined for the rectangle-shaped square lattice with various aspect ratios and various shaped triangular lattice. For the rectangle-shaped square and triangular lattices and the triangle-shaped triangular lattice, there is no logarithmic correction terms of order higher than 1/S, with S the area of the system. For the triangular lattice in rhombus, trapezoid and hexagonal shapes, there exist logarithmic correction terms of order higher than 1/S for the internal energy, and logarithmic correction terms of all orders for the specific heat.

cond-mat.stat-mech↗

arXiv2013

Phase transitions of the q-state Potts model on multiply-laced Sierpinski gaskets

We present an exact solution of the q-state Potts model on a class of generalized Sierpinski fractal lattices. The model is shown to possess an ordered phase at low temperatures and a continuous transition to the high temperature disordered phase at any q>=1. Multicriticality is observed in the presence of a symmetry-breaking field. Exact renormalization group analysis yields the phase diagram of the model and a complete set of critical exponents at various transitions.

cond-mat.dis-nn↗

arXiv2013

Skyrmion crystals in the pseudo-spin-1/2 Bose-Einstein condensates

Exact two-dimensional solutions are constructed for the pseudo-spin-1/2 Bose-Einstein condensates which are described by the coupled nonlinear Gross-Pitaevskii equations where the intraspecies and interspecies coupling constants are assumed to be equal. The equations are decoupled by means of re-combinations of the nonlinear terms of the hyperfine states according to the spatial dimensions. These stationary solutions form various spin textures which are identified as skyrmion crystals. In a special case, the crystal of skyrmion-antiskyrmion pairs is formed in the soliton limit.

cond-mat.quant-gas↗

arXiv2013

Extended Bose-Hubbard model with pair hopping on the triangular lattice

We study systematically an extended Bose-Hubbard model on the triangular lattice by means of a meanfield method based on the Gutzwiller ansatz. Pair hopping terms are explicitly included and a three-body constraint is applied. The ground-state phase diagram and a variety of quantum phase transitions are investigated in great detail. In particular, we show the existence and stability of the pair supersolid phase.

cond-mat.quant-gas↗

arXiv2013

Ising-like transitions in the O($n$) loop model on the square lattice

We explore the phase diagram of the O($n$) loop model on the square lattice in the $(x,n)$ plane, where $x$ is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling. We express the correlation length associated with the staggered loop density in the transfer-matrix eigenvalues. The finite-size data for this correlation length, combined with the scaling formula, reveal the location of critical lines in the diagram. For $n>>2$ we find Ising-like phase transitions associated with the onset of a checkerboard-like ordering of the elementary loops, i.e., the smallest possible loops, with the size of an elementary face, which cover precisely one half of the faces of the square lattice at the maximum loop density. In this respect, the ordered state resembles that of the hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of $n$ represents a softening of its particle-particle potentials. We also determine critical points in the range $-2\leq n\leq 2$. It is found that the topology of the phase diagram depends on the set of allowed vertices of the loop model. Depending on the choice of this set, the $n>2$ transition may continue into the dense phase of the $n \leq 2$ loop model, or continue as a line of $n \leq 2$ O($n$) multicritical points.

cond-mat.stat-mech↗

arXiv2012

Phase transitions in the frustrated Ising model on the square lattice

We consider the thermal phase transition from a paramagnetic to stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J1<0 (nearest neighbor, ferromagnetic) and J2 >0 (second neighbor, antiferromagnetic). The striped phase breaks a Z4 symmetry and is stabilized at low temperatures for g=J2/|J1|>1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [PRL 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The J1-J2 model has a line of very weak first-order phase transitions in the whole region 1/2 1/2. Most of our results are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological bench-marks for weakly first-order behaviors and Ashkin-Teller criticality.

cond-mat.stat-mech↗

arXiv2012

Shape dependent finite-size effect of critical two-dimensional Ising model on a triangular lattice

Using the bond-propagation algorithm, we study the finite-size behavior of the critical two-dimensional Ising model on a finite triangular lattice with free boundaries in five shapes: triangle, rhombus, trapezoid, hexagon and rectangle. The critical free energy, internal energy and specific heat are calculated. The accuracy of the free energy reaches $10^{-26}$. Based on accurate data on several finite systems with linear size up to N=2000, we extract the bulk, surface and corner parts of the free energy, internal energy and specific heat accurately. We confirm the conformal field theory prediction of the corner free energy to be universal and find logarithmic corrections in higher order terms in the critical free energy for the rhombus, trapezoid, and hexagon shaped systems, which are absent for the triangle and rectangle shaped systems. The logarithmic edge corrections due to edges parallel or perpendicular to the bond directions in the internal energy are found to be identical, while the logarithmic edge corrections due to corresponding edges in the free energy and the specific heat are different. The corner internal energy and corner specific heat for angles $π/3$, $π/2$ and $2π/3$ are obtained, as well as higher order corrections. Comparing with the corner internal energy and corner specific heat previously found on a rectangle of the square lattice (Phys. Rev. E. 86 041149 (2012)), we conclude that the corner internal energy and corner specific heat for the rectangle shape are not universal.

cond-mat.stat-mech↗

arXiv2012

Pair supersolid of the extended Bose-Hubbard model with atom-pair hopping on the triangular Lattice

We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale Quantum Monte Carlo simulations, the ground-state phase diagram are studied. We find a continuous transition between the atomic superfluid phase and the pair superfluid when the ratio of the atomic hopping and the atom-pair hopping is adapted. We then focus on the interplay among the atom-pair hopping, the on-site repulsion and the nearest-neighbor repulsion. With on-site repulsion present, we observe first order transitions between the Mott Insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with 2/3, 1 and 4/3-filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasi hardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. The transition between the pair supersolid and the pair superfluid is first order, except for the particle-hole symmetric point. We compare the results with those obtained by means of mean-field analysis.

cond-mat.quant-gas↗

arXiv2012

Finite size behaviors of critical Ising model on a rectangle with free boundaries

Using the bond-propagation algorithm, we study the Ising model on a rectangle of size $M \times N$ with free boundaries. For five aspect ratios $ρ=M/N=1,2,4,8,16$, the critical free energy, internal energy and specific heat are calculated. The largest size reached is $M \times N=64\times 10^6$. The accuracy of the free energy reaches $10^{-26}$. Basing on these accurate data, we determine exact expansions of the critical free energy, internal energy and specific heat. With these expansions, we extract the bulk, surface and corner parts of free energy, internal energy and specific heat. The fitted bulk free energy density is given by $f_{\infty}=0.92969539834161021499(1)$, comparing with Onsager's exact result $f_{\infty}=0.92969539834161021506...$. We prove the conformal field theory(CFT) prediction of the corner free energy, in which the central charge of the Ising model is found to be $c=0.5\pm 1\times 10^{-10}$ comparing with the CFT result $c=0.5$. We find that not only the corner free energy but also the corner internal energy and specific heat are geometry independent, i.e., independent of aspect ratio. The implication of this finding on the finite scaling is discussed. In the second order correction of the free energy, we prove the geometry dependence predicted by CFT and find out a geometry independent constant beyond CFT. High order corrections are also obtained.

cond-mat.stat-mech↗

arXiv2012

Critical manifold of the Potts model: Exact results and homogeneity approximation

The $q$-state Potts model has stood at the frontier of research in statistical mechanics for many years. In the absence of a closed-form solution, much of the past efforts have focused on locating its critical manifold, trajectory in the parameter $\{q, e^J\}$ space where $J$ is the reduced interaction, along which the free energy is singular. However, except in isolated cases, antiferromagnetic (AF) models with $J<0$ have been largely neglected. In this paper we consider the Potts model with AF interactions focusing on deducing its critical manifold in exact and/or closed-form expressions. We first re-examine the known critical frontiers in light of AF interactions. For the square lattice we confirm the Potts self-dual point to be the sole critical point for $J>0$. We also locate its critical frontier for $J<0$ and find it to coincide with a solvability condition observed by Baxter in 1982. For the honeycomb lattice we show that the known critical point holds for {all} $J$, and determine its critical $q_c = \frac 1 2 (3+\sqrt 5) = 2.61803$ beyond which there is no transition. For the triangular lattice we confirm the known critical point to hold only for $J>0$. More generally we consider the centered-triangle (CT) and Union-Jack (UJ) lattices consisting of mixed $J$ and $K$ interactions, and deduce critical manifolds under homogeneity hypotheses. For K=0 the CT lattice is the diced lattice, and we determine its critical manifold for all $J$ and find $q_c = 3.32472$. For K=0 the UJ lattice is the square lattice and from this we deduce both the $J>0$ and $J<0$ critical manifolds and find $q_c=3$ for the square lattice. Our theoretical predictions are compared with recent tensor-based numerical results and Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2012

Exact critical points of the O($n$) loop model on the martini and the 3-12 lattices

We derive the exact critical line of the O($n$) loop model on the martini lattice as a function of the loop weight $n$.A finite-size scaling analysis based on transfer matrix calculations is also performed.The numerical results coincide with the theoretical predictions with an accuracy up to 9 decimal places. In the limit $n\to 0$, this gives the exact connective constant $μ=1.7505645579...$ of self-avoiding walks on the martini lattice. Using similar numerical methods, we also study the O($n$) loop model on the 3-12 lattice. We obtain similarly precise agreement with the exact critical points given by Batchelor [J. Stat. Phys. 92, 1203 (1998)].

cond-mat.stat-mech↗

arXiv2010

Crossover phenomena involving the dense O($n$) phase

We explore the properties of the low-temperature phase of the O($n$) loop model in two dimensions by means of transfer-matrix calculations and finite-size scaling. We determine the stability of this phase with respect to several kinds of perturbations, including cubic anisotropy, attraction between loop segments, double bonds and crossing bonds. In line with Coulomb gas predictions, cubic anisotropy and crossing bonds are found to be relevant and introduce crossover to different types of behavior. Whereas perturbations in the form of loop-loop attractions and double bonds are irrelevant, sufficiently strong perturbations of these types induce a phase transition of the Ising type, at least in the cases investigated. This Ising transition leaves the underlying universal low-temperature O($n$) behavior unaffected.

cond-mat.stat-mech↗

arXiv2010

Hardcore bosons on the dual of the bowtie lattice

We study the zero temperature phase diagram of hardcore bosons on the dual of the bowtie lattice. Two types of striped diagonal long-range order (striped order I and striped order II) are discussed. A state with type-II striped order and superfluidity is found, even without nearest-neighbor repulsion. The emergence of such a state is due to the inhomogeneity and the anisotropy of the lattice structure. However, neither the translational symmetry nor the symmetry between sublattices of the original lattice is broken. In this paper, we restrict a 'solid state' of lattice bosons as a diagonal long-range ordered state breaking either the translational symmetry of the original lattice or the symmetry of different sublattices. We thus name such a phase a striped superfluid phase (SSF). In the presence of a nearest-neighbor repulsion, we find two striped charge density wave phases(SCDW I and II) with boson density $ρ=1/2$ (with striped order I) and $ρ=2/3$ (with striped order II) respectively, when the hopping amplitude is small compared with the repulsion. The SCDW I state is a solid, in which the translational symmetry of the original lattice is broken. We observe a rather special first-order phase transition showing an interesting multi-loop hysteresis phenomenon between the two SCDW phases when the hopping term is small enough. This can be accounted for by the special degeneracy of the ground states near the classical limit. The SSF re-appears outside the two SCDW phases. The transition between the SCDW I and SSF phases is first order, while the transition between SCDW II and SSF phases is continuous. We find that the superfluid stiffness is anisotropic in the SSF states with and without repulsion. In the SSF with repulsion, the superfluid stiffness is subject to different types of anisotropy in the region near half filling and above 2/3-filling.

cond-mat.str-el↗

arXiv2010

Effects of edge disorder in nano-scale antiferromagnetic clusters

We study the distribution of local magnetic susceptibilities in the two-dimensional antiferromagnetic S=1/2 Heisenberg model on various random clusters, in order to determine whether effects of edge disorder could be detected in NMR experiments (through the line shape, as given by the distribution of local Knight shifts). Although the effects depend strongly on the nature of the edge and the cluster size, our results indicate that line widths broader than the average shift should be expected even in clusters as large as $\approx 1000$ lattice spacing in diameter. Experimental investigations of the NMR line width should give insights into the magnetic structure of the edges.

cond-mat.str-el↗

arXiv2010

Critical frontier for the Potts and percolation models on triangular-type and kagome-type lattices II: Numerical analysis

In a recent paper (arXiv:0911.2514), one of us (FYW) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu's result is exact, and for the kagome-type lattices Wu's expression is under a homogeneity assumption. The purpose of the present paper is two-fold: First, an essential step in Wu's analysis is the derivation of lattice-dependent constants $A, B, C$ for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Secondly, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the $q$-state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices $(n\times n):(n\times n)$, $n\leq 4$, for which the exact solution is not known. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical determination of critical thresholds is accurate to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices $(1\times 1):(n\times n)$ for $1\leq n \leq 6$.

cond-mat.stat-mech↗

arXiv2009

Conducting-angle-based percolation in the XY model

We define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting angle. The percolation properties of this model are studied by means of Monte Carlo simulations and a finite-size scaling analysis. Our simulations show the existence of percolation transitions when the conducting angle is varied, and we determine the transition point for several values of the XY coupling. It appears that the critical behavior of this percolation model can be well described by the standard percolation theory. The critical exponents of the percolation transitions, as determined by finite-size scaling, agree with the universality class of the two-dimensional percolation model on a uniform substrate. This holds over the whole temperature range, even in the low-temperature phase where the XY substrate is critical in the sense that it displays algebraic decay of correlations.

cond-mat.stat-mech↗

arXiv2009

Phase transitions in self-dual generalizations of the Baxter-Wu model

We study two types of generalized Baxter-Wu models, by means of transfer-matrix and Monte Carlo techniques. The first generalization allows for different couplings in the up- and down triangles, and the second generalization is to a $q$-state spin model with three-spin interactions. Both generalizations lead to self-dual models, so that the probable locations of the phase transitions follow. Our numerical analysis confirms that phase transitions occur at the self-dual points. For both generalizations of the Baxter-Wu model, the phase transitions appear to be discontinuous.

cond-mat.stat-mech↗