Line Of Continuous Transitions Research Articles

Ensemble inequivalence in an extended spin-1 Nagle-Kardar model

We conduct a comprehensive investigation of an extended spin-1 Nagle-Kardar model in the microcanonical ensemble, focusing on exploring the inequivalence between the canonical and microcanonical ensembles in this generalized model. Our results reveal that the general trends of the microcanonical phase diagram align with those in the canonical ensemble. The continuous phase transition lines of these two ensembles largely coincide, yet the first-order ones in the microcanonical ensemble exhibit greater complexity, showing various examples of ensemble inequivalence, particularly in cases involving the triple points.

Design of continuous transition line pattern between layers of composite pressure vessel

To realize efficient and stable continuous transition between different winding process layers of composite pressure vessels. This article uses the non-geodesic winding equation to propose a transition layer design method for composite pressure vessel shells with circular cross-section core molds and ellipsoidal heads. Firstly, the fourth-order Runge–Kutta method is used to solve the non-geodesic stabilized winding pattern and then analyze different regions’ transition ability. Established a calculation model to determine the corresponding transition winding trajectory according to the known core mold shape and fiber position and carried out computer image simulation of different modes of transition layer patterns, and finally carried out experimental verification of 35 MPa composite pressure vessel based on the simulation. The results show that different regions of the core mold have different abilities to change different starting winding angles, and the design of the transition process layer based on this law can save the area needed for transition. This method realizes the smooth transition of different process layers; the fiber of the transition layer does not slip in the actual winding process, and the actual pattern of the winding is consistent with the simulation results, which saves 20.8% of the winding time, and effectively improves the automation of the composite pressure vessel winding process.

Critical behaviour near critical end points and tricritical points in disordered spin-1 ferromagnets

Critical end points and tricritical points are multicritical points that separate lines of continuous transitions from lines of first order transitions in the phase diagram of many systems. In models like the spin-1 disordered Blume–Capel model and the repulsive Blume–Emery–Griffiths model, the tricritical point splits into a critical end point and a bicritical end point with an increase in disorder and repulsive coupling strength respectively. In order to make a distinction between these two multicritical points, we investigate and contrast the behaviour of the first order phase boundary and the co-existence diameter around them.

Dissipative phase transitions in optomechanical systems

We show that optomechanical quantum systems can undergo dissipative phase transitions within the limit of a small nonlinear interaction and strong external drive. In such a defined thermodynamical limit, the nonlinear interaction stabilizes optomechanical dynamics in strong- and ultrastrong-coupling regimes. As a consequence, optomechanical systems possess a rich phase diagram consisting of periodic orbits and discontinuous and continuous dissipative phase transitions with and without bifurcation. We also find a critical point where continuous and discontinuous dissipative phase transition lines meet. Our analysis demonstrates that optomechanical systems are valuable for understanding the rich physics of dissipative phase transitions and ultrastrong-coupling regimes.

Ising model on a 2D additive small-world network

In this article, we have employed Monte Carlo simulations to study the Ising model on a two-dimensional additive small-world network (A-SWN). The system model consists of a LxL square lattice where each site of the lattice is occupied for a spin variable that interacts with the nearest neighbor and has a certain probability p of being additionally connected at random to one of its farther neighbors. The system is in contact with a heat bath at a given temperature T and it is simulated by one-spin flip according to the Metropolis prescription. We have calculated the thermodynamic quantities of the system, such as, the magnetization per spin m, magnetic susceptibility chi, and the reduced fourth-order Binder cumulant U as a function of T for several values of lattice size L and additive probability p. We also have constructed the phase diagram for the equilibrium states of the model in the plane T versus p showing the existence of a continuous transition line between the ferromagnetic F and paramagnetic P phases. Using the finite-size scaling (FSS) theory, we have obtained the critical exponents for the system, where varying the parameter p, we have observed a change in the critical behavior from the regular square lattice Ising model to A-SWN.

Multicritical point of the three-dimensional Z2 gauge Higgs model

We investigate the multicritical behavior of the three-dimensional ${\mathbb{Z}}_{2}$ gauge Higgs model at the multicritical point (MCP) of its phase diagram, where one first-order transition line and two continuous Ising-like transition lines meet. The duality properties of the model determine some features of the multicritical behavior at the MCP located along the self-dual line. Moreover, we argue that the system develops a multicritical $XY$ behavior at the MCP, which is controlled by the stable $XY$ fixed point of the three-dimensional multicritical Landau-Ginzburg-Wilson field theory with two competing scalar fields associated with the continuous ${\mathbb{Z}}_{2}$ transition lines meeting at the MCP. This implies an effective enlargement of the symmetry of the multicritical modes at the MCP to the continuous group O(2). We also provide numerical results to support the multicritical $XY$ scenario.

Topological quantum critical points in strong coupling limits: Global symmetries and strongly interacting Majorana fermions

In this paper, we discuss strong coupling limits of topological quantum critical points (TQCPs) where quantum phase transitions between two topological distinct superconducting states take place. We illustrate that while superconducting phases on both sides of TQCPs spontaneously break the same symmetries, universality classes of critical states can be identified only when global symmetries in topological states are further specified. In dimensions $d=2\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}3$, we find that continuous $(d+1)\mathrm{th}$-order transitions at weakly interacting TQCPs that were pointed out previously in the presence of the emergent Lorentz symmetry can be terminated by strongly interacting fixed points of Majorana fields. For $2d$ time reversal symmetry breaking TQCPs, termination points are supersymmetric with $\mathcal{N}=4{N}_{f}=1$ (where ${N}_{f}$ is the number of four-component Dirac fermions and $\mathcal{N}$ is the number of two-component real fermions) beyond which transitions are discontinuous first-order ones. For $2d$ time reversal symmetric TQCPs without other global symmetries, termination points of $(d+1)\mathrm{th}$-order continuous transition lines are generically conformal invariant without supersymmetry. Beyond these strong coupling fixed points, there are first-order discontinuous transitions as far as the protecting symmetry is not spontaneously broken but no direct transitions if the protecting symmetry is spontaneously broken in the presence of strong interactions. In this case, termination points can become supersymmetric with $\mathcal{N}=4{N}_{f}=2$ only when interacting Majorana fermions further display an emergent global $\text{U}(1)$ symmetry. In $3d$, strong coupling termination points can be further effectively represented by new emergent gapless real bosons weakly coupled with free gapless Majorana fermions. However, in $1d$, time reversal symmetric $(d+1)\mathrm{th}$ continuous transition lines of TQCPs are terminated by simple free Majorana fermion fixed points.

Lattice gauge theories in the presence of a linear gauge-symmetry breaking.

We study the effects of gauge-symmetry breaking (GSB) perturbations in three-dimensional lattice gauge theories with scalar fields. We study this issue at transitions in which gauge correlations are not critical and the gauge symmetry only selects the gauge-invariant scalar degrees of freedom that become critical. A paradigmatic model in which this behavior is realized is the lattice CP^{1} model or, more generally, the lattice Abelian-Higgs model with two-component complex scalar fields and compact gauge fields. We consider this model in the presence of a linear GSB perturbation. The gauge symmetry turns out to be quite robust with respect to the GSB perturbation: the continuum limit is gauge invariant also in the presence of a finite small GSB term. We also determine the phase diagram of the model. It has one disordered phase and two phases that are tensor and vector ordered, respectively. They are separated by continuous transition lines, which belong to the O(3), O(4), and O(2) vector universality classes, and which meet at a multicritical point. We remark that the behavior at the CP^{1} gauge-symmetric critical point substantially differs from that at transitions in which gauge correlations become critical, for instance at transitions in the noncompact lattice Abelian-Higgs model that are controlled by the charged fixed point: in this case, the behavior is extremely sensitive to GSB perturbations.

Multifunctional twisted kagome lattices: Tuning by pruning mechanical metamaterials.

This article investigates phonons and elastic response in randomly diluted lattices constructed by combining (via the addition of next-nearest bonds) a twisted kagome lattice, with bulk modulus B=0 and shear modulus G>0, with either a generalized untwisted kagome lattice with B>0 and G>0 or with a honeycomb lattice with B>0 and G=0. These lattices exhibit jamming-like critical endpoints at which B,G, or both B and G jump discontinuously from zero while the remaining moduli (if any) begin to grow continuously from zero. Pairs of these jamming points are joined by lines of continuous rigidity percolation transitions at which both B and G begin to grow continuously from zero. The Poisson ratio and G/B can be continuously tuned throughout their physical range via random dilution in a manner analogous to "tuning by pruning" in random jammed lattices. These lattices can be produced with modern techniques, such as three-dimensional printing, for constructing metamaterials.

Phase transitions of ordered ice in graphene nanocapillaries and carbon nanotubes

New phase diagrams for water confined in graphene nanocapillaries and single-walled carbon nanotubes (CNTs) are proposed, identifying ice structures, their melting points and revealing the presence of a solid-liquid critical point. For quasi-2D water in nanocapillaries, we show through molecular-dynamics simulations that AA stacking in multilayer quasi-2D ice arises from interlayer hydrogen-bonding and is stable up to three layers, thereby explaining recent experimental observations. Detailed structural and energetic analyses show that quasi-2D water can freeze discontinuously through a first-order phase transition or continuously with a critical point. The first-order transition line extends to a continuous transition line, defined by a sharp transition in diffusivity between solid-like and liquid-like regimes. For quasi-1D water, confined in CNTs, we observe the existence of a similar critical point at intermediate densities. In addition, an end point is identified on the continuous-transition line, above which the solid and liquid phases deform continuously. The solid-liquid phase transition temperatures in CNTs are shown to be substantially higher than 273 K, confirming recent Raman spectroscopy measurements. We observe ultrafast proton and hydroxyl transport in quasi-1D and -2D ice at 300 K, exceeding those of bulk water up to a factor of five, thereby providing possible applications to fuel-cells and electrolyzers.

Disappearance of the Hexatic Phase in a Binary Mixture of Hard Disks.

Recent studies of melting in hard disks have confirmed the existence of a hexatic phase occurring in a narrow window of density which is separated from the isotropic liquid phase by a first-order transition, and from the solid phase by a continuous transition. However, little is known concerning the melting scenario in mixtures of hard disks. Here we employ tailored MonteCarlo simulations to elucidate the phase behavior of a system of large (l) and small (s) disks with diameter ratio σ_{l}/σ_{s}=1.4. We find that as small disks are introduced to a system of large ones, the stability window of the hexatic phase shrinks progressively until the line of continuous transitions terminates at an end point beyond which melting becomes a first-order liquid-solid transition. This occurs at surprisingly low concentrations of the small disks, c≲1%, emphasizing the fragility of the hexatic phase. We speculate that the change to the melting scenario is a consequence of strong fractionation effects, the nature of which we elucidate.

Critical behavior of the extended Hubbard model with bond dimerization

Exploiting the matrix-product-state based density-matrix renormalization group (DMRG) technique we study the one-dimensional extended (U-V) Hubbard model with explicit bond dimerization in the half-filled band sector. In particular we investigate the nature of the quantum phase transition, taking place with growing ratio V/U between the symmetry-protected-topological and charge-density-wave insulating states. The (weak-coupling) critical line of continuous Ising transitions with central charge c=1/2 terminates at a tricritical point belonging to the universality class of the dilute Ising model with c=7/10. We demonstrate that our DMRG data perfectly match with (tricritical) Ising exponents, e.g., for the order parameter β=1/8 (1/24) and correlation length ν=1 (5/9). Beyond the tricritical Ising point, in the strong-coupling regime, the quantum phase transition becomes first order.

First-order transition in a percolation model with nucleation and preferential growth.

The spanning cluster properties of a percolation model with nucleation and preferential growth exhibit first-order transitions depending on the values of the growth parameter g_{0} and the initial seed concentration ρ. Except for the preferential growth of smaller clusters with a size-dependent growth probability of amplitude g_{0}, the model preserves all other criteria of the original percolation model. As ρ decreases starting from the percolation threshold p_{c} of the original percolation, a line of continuous transition encounters a coexistence region of percolative and nonpercolative large clusters. At sufficiently small values of ρ (≤0.05), the value of g_{0} exceeds p_{c} and generates compact spanning clusters leading to first-order discontinuous transitions.

Absence of first order transition in the random crystal field Blume–Capel model on a fully connected graph

In this paper we solve the Blume–Capel model on a complete graph in the presence of random crystal field with a distribution, , using large deviation techniques. We find that the first order transition of the pure system is destroyed for 0.046 < p < 0.954 for all values of the crystal field, . The system has a line of continuous transition for this range of p from . For values of p outside this interval, the phase diagram of the system is similar to the pure model, with a tricritical point separating the line of first order and continuous transitions. We find that in this regime, the order vanishes for large for p < 0.046(and for large for p > 0.954) even at zero temperature.

Incommensurate-commensurate transitions in the monoaxial chiral helimagnet driven by the magnetic field

The zero-temperature phase diagram of the monoaxial chiral helimagnet in the magnetic-field plane formed by the components parallel and perpendicular to the helical axis is thoroughly analyzed. The nature of the transition to the commensurate state depends on the angle between the field and the helical axis. For field directions close to the directions parallel or perpendicular to the helical axis the transition is continuous, while for intermediate angles the transition is discontinuous and the incommensurate and commensurate states coexist on the transition line. The continuous and discontinuous transition lines are separated by two tricritical points with specific singular behavior. The location of the continuous and discontinuous lines and of the tricritical points depend strongly on the easy-plane anisotropy, the effect of which is analyzed. For high anisotropy the conical approximation locates the transition line very accurately, although it does not predict the continuous transitions and the tricritical behavior. It is shown that for high anisotropy, as in ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$, the form of the transition line is universal, that is, independent of the sample, and obeys a simple equation. The position of the tricritical points, which is not universal, is theoretically estimated for a sample of ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$.

Nature of the collapse transition in interacting self-avoiding trails.

We study the interacting self-avoiding trail (ISAT) model on a Bethe lattice of general coordination q and on a Husimi lattice built with squares and coordination q=4. The exact grand-canonical solutions of the model are obtained, considering that up to K monomers can be placed on a site and associating a weight ω_{i} with an i-fold visited site. Very rich phase diagrams are found with nonpolymerized, regular polymerized, and dense polymerized phases separated by lines (or surfaces) of continuous and discontinuous transitions. For a Bethe lattice with q=4 and K=2, the collapse transition is identified with a bicritical point and the collapsed phase is associated with the dense polymerized (solidlike) phase instead of the regular polymerized (liquidlike) phase. A similar result is found for the Husimi lattice, which may explain the difference between the collapse transition for ISATs and for interacting self-avoiding walks on the square lattice. For q=6 and K=3 (studied on the Bethe lattice only), a more complex phase diagram is found, with two critical planes and two coexistence surfaces, separated by two tricritical and two critical end-point lines meeting at a multicritical point. The mapping of the phase diagrams in the canonical ensemble is discussed and compared with simulational results for regular lattices.

Mean-field solution of the Blume–Capel model under a random crystal field

In this work we investigate the Blume–Capel model with infinite-range ferromagnetic interactions and under the influence of a quenched disorder – a random crystal field. For a suitable choice of the random crystal field the model displays a wealth of multicritical behavior, continuous and first-order transition lines, as well as re-entrant behavior. The resulting phase diagrams show a variety of topologies as a function of the disorder parameter p. A comparison with recent results on the Blume–Capel model in random crystal field is discussed.

Discontinuous transition of a multistage independent cascade model on networks

We propose a multistage version of the independent cascade model, which we call a multistage independent cascade (MIC) model, on networks. This model is parameterized by two probabilities: the probability T1 that a node adopting a fad increases the awareness of a neighboring susceptible node and the probability T2 that an adopter directly causes a susceptible node to adopt the fad. We formulate a tree approximation for the MIC model on an uncorrelated network with an arbitrary degree distribution pk. Applied on a random regular network with degree k = 6, this model exhibits a rich phase diagram, including continuous and discontinuous transition lines for fad percolation and a continuous transition line for the percolation of susceptible nodes. In particular, the percolation transition of fads is discontinuous (continuous) when T1 is larger (smaller) than a certain value. A similar discontinuous transition is observed in random graphs and scale-free networks. Furthermore, assigning a finite fraction of initial adopters dramatically changes the phase boundaries.

Monte Carlo simulations of polymers with nearest- and next nearest-neighbor interactions on square and cubic lattices

We study a generalized interacting self-avoiding walk (ISAW) model with nearest- and next nearest-neighbor (NN and NNN) interactions on square and cubic lattices. In both dimensions, the phase diagrams show coil and globule phases separated by continuous transition lines. Along these lines, we calculate the metric νt, crossover ϕt and entropic γt exponents, all of them in good agreement with the exact values of the Θ universality class. Therefore, the introduction of NNN interactions does not change the class of the ISAW model, which still exists even for repulsive forces. The growth parameters μt are shown to change monotonically with temperature along the Θ-lines. In the square lattice, the Θ-line has an almost linear behavior, which was not found in the cubic one. Although the region of repulsive NNN interactions, with attractive NN ones, leads to stiff polymers, no evidence of a transition to a crystalline phase was found.

Global analysis of the ground-state wrapping conformation of a charged polymer on an oppositely charged nano-sphere

We investigate the wrapping conformations of a single, strongly adsorbed polymer chain on an oppositely charged nano-sphere by employing a reduced (dimensionless) representation of a primitive chain-sphere model. This enables us to determine the global behavior of the chain conformation in a wide range of values for the system parameters including the chain contour length, its linear charge density and persistence length as well as the nano-sphere charge and radius, and also the salt concentration in the bathing solution. The structural behavior of a charged chain-sphere complex can be described in terms of a few distinct conformational symmetry classes separated by continuous or discontinuous transition lines which are determined by means of appropriately defined (order) parameters. Our results can be applied to a wide class of strongly coupled polymer-sphere complexes including, for instance, complexes that comprise a mechanically flexible or semiflexible polymer chain or an extremely short or long chain and, as a special case, include the biologically relevant example of DNA-histone complexes.