M. Danco, J. Strecka
Ground-state phase diagram of the mixed spin-$1/2$ and spin-$1$ Ising chain with axial and rhombic zero-field splitting parameters is exactly calculated within the framework of the transfer-matrix method. It is shown that the rhombic zero-field splitting parameter prefers the magnetically ordered phase instead of the disordered phase.
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The mixed spin-(1/2,1) Ising chain with axial and rhombic zero-field splitting parameters in a presence of the longitudinal magnetic field is exactly solved within the framework of decoration-iteration transformation and transfer-matrix method. Our particular emphasis is laid on an investigation of the influence of the rhombic term, which is responsible for an onset of quantum entanglement between two magnetic states S_k^z = 1 and -1 of the spin-1 atoms. It is shown that the rhombic term gradually destroys a classical ferrimagnetic order in the ground state and simultaneously causes diversity …
The axial next-nearest-neighbor Ising model is studied in two dimensions at finite temperature using the density matrix renormalization group. The model exhibits phase transition of the second-order between the antiphase in low temperature and the modulated phase in high temperature. Observing the domain wall free energy, we confirm that the modulation period in high-temperature side is well explained by the free-fermion picture.
The three-dimensional axial-next-nearest-neighbor Ising (ANNNI) model is studied by a modified tensor product variational approach (TPVA). A global phase diagram is constructed with numerous commensurate and incommensurate magnetic structures. The devil's stairs behavior for the model is confirmed. The wavelength of the spin modulated phases increases to infinity at the boundary with the ferromagnetic phase. Widths of the commensurate phases are considerably narrower than those calculated by mean-field approximations.
An axial next-nearest-neighbor Ising (ANNNI) model is studied by using the non-equilibrium relaxation method. We find that the incommensurate stripe phase between the ordered phase and the paramagnetic phase is negligibly narrow or may vanish in the thermodynamic limit. The phase transition is the second-order transition if approached from the ordered phase, and it is of the Kosterlitz-Thouless type if approached from the paramagnetic phase. Both transition temperatures coincide with each other within the numerical errors. The incommensurate phase which has been observed previously is a parama…
Uniaxially anisotropic Heisenberg ferromagnet, in the presence of a magnetic fieldvarying sinusoidally in time, is studied by Monte Carlo Simulation. The axial (field applied only along the direction of anisotropy) and off-axial (field applied only along the direction which is prependicular to the direction of anisotropy) dynamic transitions are studied. By studying the distribution of the dynamic order parameter component, it is observed that the axial transition is discontinuous for low anisotropy and becomes continuous in high anisotropy. The off-axial transition is found to be continuous f…
We show here for the one-dimensional spin-1/2 ANNNI (axial-next-to-nearest-neighbor-Ising) model in an external magnetic field that the linear density of Yang-Lee zeros may diverge with critical exponent $σ= -2/3$ at the Yang-Lee edge singularity. The necessary condition for this unusual behavior is the triple degeneracy of the transfer matrix eigenvalues. If this condition is absent we have the usual value $σ= -1/2$. Analogous results have been found in the literature in the spin-1 Blume-Emery-Griffths model and in the three-state Potts model in a magnetic field with two complex components. O…
The equilibrium phase behavior of microphase-forming systems is notoriously difficult to obtain because of the extended metastability of their modulated phases. In this paper we present a systematic simulation methodology for studying layered microphases and apply the approach to two prototypical lattice-based systems: the three-dimensional axial next-nearest-neighbor Ising (ANNNI) and Ising-Coulomb (IC) models. The method involves thermodynamically integrating along a reversible path established between a reference system of free spins under an ordering field and the system of interest. The r…
The equilibrium phase behavior of microphase-forming substances and models is notoriously difficult to obtain because of the extended metastability of the modulated phases. We develop a simulation method based on thermodynamic integration that avoids this problem and with which we obtain the phase diagram of the canonical three-dimensional axial next-nearest-neighbor Ising model. The equilibrium devil's staircase, magnetization, and susceptibility are obtained. The critical exponents confirm the XY nature of the disorder-modulated phase transition beyond the Lifshitz point. The results identif…
Ground state properties of the one-dimensional axial next-nearest-neighbor Ising model in a transverse field
针对横场下一维ANNNI模型的阻挫相表征难题，采用模式图景分析不同尺寸周期边界系统的基态，明确了四类基态相及相变类型，验证了图景的有效性。
Using the transfer matrix method for Axial Next-Nearest Neighbor Ising model without an external field on a closed chain of spins of width 2 in the direction of interaction of only nearest neighbors and length L in the direction of interaction of nearest neighbors and next nearest neighbors, we found exact values of the partition function in a finite strip of length L , free energy, internal energy per node, heat capacity in a finite strip of length L and in the thermodynamic limit. The entire spectrum of the 16x16 transfer matrix and the structure of all transfer matrix eigenvectors are found…
We investigate sudden quenches across the critical point in the transverse field Ising chain with a perturbing non-integrable next-nearest-neighbour interaction. Expressions for the return (Loschmidt) amplitude and associated rate function are derived to linear order in the next-nearest-neighbour coupling. In the thermodynamic limit these quantities exhibit non-analytic behaviour at a set of critical times, a phenomenon referred to as a dynamical quantum phase transition. We quantify the effect of the integrability breaking perturbation on the location and shape of these non-analyticities. Our…
The axial next-nearest-neighbour Ising (ANNNI) model of finite thickness is studied. Using mean-field theory, Monte Carlo simulations, and low-temperature analyses, phase diagrams are determined, with a distinct phase diagram for each film thickness. The robustness of the phase diagrams against varying the couplings in the surface layers is analysed.
We study the anisotropic Heisenberg (XYZ) spin-1/2 chain placed in a magnetic field pointing along the x-axis. We use bosonization and a renormalization group analysis to show that the model has a non-trivial fixed point at a certain value of the XY anisotropy a and the magnetic field h. Hence, there is a line of critical points in the (a,h) plane on which the system is gapless, even though the Hamiltonian has no continuous symmetry. The quantum critical line corresponds to a spin-flop transition; it separates two gapped phases in one of which the Z_2 symmetry of the Hamiltonian is broken. Our…
In order to provide an experimental access to the statistical theory of Lee and Yang (1952) the density function g(theta) of zeros on the Lee-Yang circle has been determined for the first time by analyzing isothermal magnetization data, m(H), of the Ising ferromagnet FeCl2 in axial magnetic fields, H, at temperatures 34 < T < 99K. The validity of our approach is demonstrated by the perfect agreement of magnetic specific heat data as calculated from g(theta) and m(H) via Maxwells relation, respectively. Moreover, the correct in-plane exchange constant of FeCl2 emerges from the series expansion …
We investigate the phase diagram of a spin-$1/2$ Ising model on a cubic lattice, with competing interactions between nearest and next-nearest neighbors along an axial direction, and fully connected spins on the sites of each perpendicular layer. The problem is formulated in terms of a set of noninteracting Ising chains in a position-dependent field. At low temperatures, as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising (ANNNI) model, there are many distinct spatially commensurate phases that spring from a multiphase point of infinitely degenerate ground states. As …
Phase transitions of the mixed spin-1/2 and spin-S (S >= 1/2) Ising model on a three-dimensional (3D) decorated lattice with a layered magnetic structure are investigated within the framework of a precise mapping relationship to the simple spin-1/2 Ising model on the tetragonal lattice. This mapping correspondence yields for the layered Ising model of mixed spins plausible results either by adopting the conjectured solution for the spin-1/2 Ising model on the orthorhombic lattice [Z.-D. Zhang, Philos. Mag. 87 (2007) 5309-5419] or by performing extensive Monte Carlo simulations for the correspo…
We investigate both the local and global persistence behaviour in ANNNI (axial next-nearest neighour Ising) model. We find that when the ratio $κ$ of the second neighbour interaction to the first neighbour interaction is less than 1, $P(t)$, the probability of a spin to remain in its original state upto time $t$ shows a stretched exponential decay. For $κ> 1$, $P(t)$ has a algebraic decay but the exponent is different from that of the nearest neighbour Ising model. The global persistence behaviour shows similar features. We also conduct some deeper investigations in the dynamics of the ANNNI m…
The dynamical percolation transition of two dimensional Axial Next Nearest Neighbour Ising (ANNNI) model to pulsed magnetic field has been studied by finite size scaling analysis (by Monte Carlo simulation) for various values of frustration parameters, pulse width and temperature (below the corresponding static transition temperature). It has been found that the size of the largest geometrical cluster shows a transition for a critical field amplitude. Although the transition points shift, the critical exponents remain invariant for a wide range of frustration parameters. It is also same as tha…
Ising models with frustrated next-nearest-neighbor interactions present a rich morphology of modulated phases. These phases, however, assemble and relax slowly, which hinders their computational study. In two dimensions, strong fluctuations further hamper determining their equilibrium phase behavior from theoretical approximations. The exact numerical transfer matrix (TM) method, which bypasses these difficulties, can serve as a benchmark method once its own numerical challenges are surmounted. Building on our recent study [Hu and Charbonneau, Phys. Rev. B 103, 094441 (2021)], in which we eval…
It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry breaking glass solution in the case of non-reflective symmetry diagonal operators used instead of Ising spins. As an example, axial quadrupole moments in place of Ising spins are considered and the boundary value $p_{c_{1}}\cong 2.5$ is found.
The linear perturbation group transformation (LPRG) is used to study the thermodynamics of the axial next-nearest-neighbor Ising model with four spin interactions (extended ANNNI) in a field. The LPRG for weakly interacting Ising chains is presented. The method is used to study finite field para-ferrimagnetic phase transitions observed in layered uranium compounds, UAs_{1-x}Se_x, UPd_2Si_2 or UNi_2Si_2. The above-mentioned systems are made of ferromagnetic layers and the spins from the nearest-neighbor and next-nearest-neighbor layers are coupled by the antiferromagnetic interactions J_1<0 and…
To understand the collinear-magnetism-driven ferroelectricity in multiferroic Ca3CoMnO6 compound, we have established an elastic diatomic Ising spin-chain model with axial-next-nearest-neighbor interaction to describe its magnetoelectric properties. By employing magneto-phonon decoupling and transfer-matrix method, the possible ground-state configurations and thermodynamic behaviors of the system have been exactly determined. From the perspective of the ground-state configuration, we analyze the computational results and make a detail comparison with experimental data. The parameter relation f…
The magnetization process of the spin-1 Heisenberg dimer model with axial and rhombic single-ion anisotropy terms is particularly investigated in connection with recent experimental high-field measurements performed on the single-crystal sample of the homodinuclear nickel(II) compound [Ni2(Medpt)2(ox)(H2O)2](ClO4)2.2H2O (Medpt=methyl-bis(3-aminopropyl)amine). The results obtained from the exact numerical diagonalization reveal a striking magnetization process with a marked spatial dependence on the applied magnetic field for arbitrary but non-zero single-ion anisotropy. It is demonstrated that…
We investigate the dynamics of a two dimensional axial next nearest neighbour Ising (ANNNI) model following a quench to zero temperature. The Hamiltonian is given by $H = -J_0\sum_{i,j=1}^L S_{i,j}S_{i+1,j} - J_1\sum_{i,j=1} [S_{i,j} S_{i,j+1} -κS_{i,j} S_{i,j+2}]$. For $κ<1$, the system does not reach the equilibrium ground state but slowly evolves to a metastable state. For $κ> 1$, the system shows a behaviour similar to the two dimensional ferromagnetic Ising model in the sense that it freezes to a striped state with a finite probability. The persistence probability shows algebraic decay he…
We study the effect of antiferromagnetic interactions on the single spin-flip Glauber dynamics of two different one-dimensional (1D) Ising models with spin $\pm 1$. The first model is an Ising chain with antiferromagnetic exchange interaction limited to nearest neighbors and subject to an oscillating magnetic field. The system of master equations describing the time evolution of sublattice magnetizations can easily be solved within a linear field approximation and a long time limit. Resonant behavior of the magnetization as a function of temperature (stochastic resonance) is found, at low freq…
High temperature modulations, meso-scale interactions and hyperscaling breakdown in Ising models with frustration: some insights from thermodynamic geometry
本研究重新审视A3NNI链，利用微观两点关联函数和宏观热力学曲率探测由竞争相互作用与阻挫引发的相行为，发现超标度破缺等现象，并澄清了高温关联长度的度量。
We consider the effects of a quench to T = 0 on a spin system with axial next-next nearest neighbour Ising interactions, evolving under a conserved 3-spin flip dynamics. Such a model is motivated by the kinetics of stacking layers in polytypes near the 3C-6H transition. We find that the system generically gets arrested in interesting metastable states which have inhomogeneously distributed quiescent and active regions. In such arrested states, the autocorrelation function decays as a stretched exponential $\sim \exp(-(t/τ_{o})^{1 \over 3})$. The latter feature can be understood in terms of a m…
Semi-infinite $d$-dimensional systems with an $m$-axial bulk Lifshitz point are considered whose ($d-1$)-dimensional surface hyper-plane is oriented perpendicular to one of the $m$ modulation axes. An $n$-component $ϕ^4$ field theory describing the bulk and boundary critical behaviour when (i) the Hamiltonian can be taken to have O(n) symmetry and (ii) spatial anisotropies breaking its Euclidean symmetry in the $m$-dimensional coordinate subspace of potential modulation directions may be ignored is investigated. The long-distance behaviour at the ordinary surface transition is mapped onto a fi…
We study the equilibrium and dynamical properties of the ANNNI (axial next-nearest-neighbor Ising) chain at the multiphase point. An interesting property of the system is the macroscopic degeneracy of the ground state leading to finite zero-temperature entropy. In our equilibrium study we consider the effect of softening the spins. We show that the degeneracy of the ground state is lifted and there is a qualitative change in the low temperature behaviour of the system with a well defined low temperature peak of the specific heat that carries the thermodynamic ``weight'' of the ground state ent…
We study the XYZ spin-1/2 chain placed in a magnetic field pointing along the x-axis. We use bosonization and a renormalization group analysis to show that the model has a non-trivial fixed point at a certain value of the XY anisotropy a and the magnetic field h. Hence, there is a line of critical points in the plane (a,h) on which the system is gapless, even though the Hamiltonian has no continuous symmetry. The quantum critical line separates a gapped commensurate phase from a gapped incommensurate phase. Our study explains why the floating phase of the axial next-nearest neighbor Ising (ANN…
The behaviour of the 3D axial next-nearest neighbour Ising (ANNNI) model at the uniaxial Lifshitz point is studied using Monte Carlo techniques. A new variant of the Wolff cluster algorithm permits the analysis of systems far larger than in previous studies. The Lifshitz point critical exponents are $α=0.18(2)$, $β=0.238(5)$ and $γ=1.36(3)$. Data for the spin-spin correlation function are shown to be consistent with the explicit scaling function derived from the assumption of local scale invariance, which is a generalization of conformal invariance to the anisotropic scaling {\em at} the Lifsh…
Probing the mesoscopics of competing interactions with the thermodynamic curvature: the case of a two-parameter ANNNI chain
本文通过双参数ANNNI链验证热力学曲率R作为关联体积和统计相互作用度量的猜想，并揭示介观涨落子结构特征及三阶涨落矩的关键作用。
The spin structure of an axial next-nearest-neighbor Ising (ANNNI) model in two dimensions (2D) is a renewed problem because different Monte Carlo (MC) simulation methods predicted different spin orderings. The usual equilibrium simulation predicts the occurrence of a floating incommensurate (IC) Kosterlitz-Thouless (KT) type phase, which never emerges in non-equilibrium relaxation (NER) simulations. In this paper, we first examine previously published results of both methods, and then investigate a higher transition temperature, $T_{c1}$, between the IC and paramagnetic phases. In the usual e…
We have examined the spin ordering of an axial next-nearest-neighbor Ising (ANNNI) model in two dimensions (2D) near above the antiphase ($\langle 2 \rangle$ phase). We considered an $N_R$-replica system and calculated an overlap function $q_m$ between different replicas having used a cluster heat bath (CHB) Monte Carlo method. We determined transition temperature between $\langle 2 \rangle$ phase and a floating incommensurate (IC) phase as $T_{C2}/J = 0.89 \pm 0.01$ with frustration ratio $κ(\equiv -J_2/J_1) = 0.6$. We found that the spin state at $T \gtrsim T_{C2}$ may be called as a domain …
A Human-AI Theorem Connecting Spontaneous and Field-Induced Mechanisms of Collective Behavior in One Dimension
该研究证明了连接一维统计物理学中集体行为自发与场诱导机制的人机定理，揭示了人机协作可孕育自主科学突破的可能性。
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