We consider a one-dimensional lattice of Ising-type variables where the ferromagnetic exchange interaction J between neighboring sites is frustrated by a long-ranged anti-ferromagnetic interaction of strength g between the sites i and j, decaying as |i-j|^-alpha, with alpha>1. For alpha smaller than a certain threshold alpha_0, which is larger than 2 and depends on the ratio J/g, the ground state consists of an ordered sequence of segments with equal length and alternating magnetization. The width of the segments depends on both alpha and the ratio J/g. Our Monte Carlo study shows that the on-site magnetization vanishes at finite temperatures and finds no indication of any phase transition. Yet, the modulation present in the ground state is recovered at finite temperatures in the two-point correlation function, which oscillates in space with a characteristic spatial period: The latter depends on alpha and J/g and decreases smoothly from the ground-state value as the temperature is increased. Such an oscillation of the correlation function is exponentially damped over a characteristic spatial scale, the correlation length, which asymptotically diverges roughly as the inverse of the temperature as T=0 is approached. This suggests that the long-range interaction causes the Ising chain to fall into a universality class consistent with an underlying continuous symmetry. The e^(Delta/T)-temperature dependence of the correlation length and the uniform ferromagnetic ground state, characteristic of the g=0 discrete Ising symmetry, are recovered for alpha > alpha_0.
Spontaneous order in the highly frustrated spin-1/2 Ising-Heisenberg model on the triangulated Kagome lattice due to the Dzyaloshinskii-Moriya anisotropy
Here we consider the Ising-Heisenberg model in the expanded Kagomé lattice, also known as triangle-dodecagon (3-12) or star lattice. This model can still be understood as a decorated honeycomb lattice. Assuming that the Heisenberg spins are at the vertices of the triangle while other spins are of the Ising type. Thus, this model is equivalent to an effective Kagomé Ising lattice, through the decoration transformation technique. Thus this means that the model is exactly solvable so we can study the most relevant properties of this model. Like the phase diagram at zero temperature, exhibiting a …
Critical and in the highly frustrated regime also dynamical properties of the $J_1-J_2$ Ising model with competing nearest-neighbor $J_1$ and second-nearest-neighbor $J_2$ interactions on a honeycomb lattice are investigated by standard Monte Carlo and parallel tempering simulations. The phase boundary is determined as a function of the coupling ratio for the phase transition between the paramagnetic and ferromagnetic states within $R \equiv J_2/|J_1| \in [-1/4,0]$. It is confirmed that at least for $R \geq -0.2$ the transition remains second-order and complies with the standard Ising universa…
Ashkin-Teller criticality and weak-first-order behavior of phase transition to four-fold degenerate state in two-dimensional frustrated Ising antiferromagnets
We consider itinerant spinless fermions as moving defects in a dilute two-dimensional frustrated Ising system where they occupy site vacancies. Fermions interact via local spin fluctuations and we analyze coupled self-consistent mean-field equations of the Green functions after expressing the spin and fermion operators in terms of Grassmann variables. The specific heat and effective mass are analyzed with the solutions satisfying the symmetry imposed by the coupling layout. At low temperature, we find that these solutions induce stripes along the lines of couplings with the same sign, and that…
The entanglement between spin-1/2 interstitial Heisenberg dimers in the mixed spin-(1,1/2) Ising-XXZ double sawtooth ladder is investigated at low temperature. Here, we consider a cyclic four-spin exchange interaction in square plaquette of each block, and investigate the effects of this amazing interaction on the bipartite entanglement between spin-1/2 interstitial dimers. Interestingly, we observe a remarkable difference in concurrence behavior with respect to the cyclic four-spin exchange interaction and magnetic field. Also, the critical points at which the concurrence vanishes are changed…
Magnetic frustrations and dimensionality play an important role in determining the nature of the magnetic long-range order and how it melts at temperatures above the ordering transition $T_N$. In this work, we use large-scale Monte Carlo simulations to study these phenomena in a class of frustrated Ising spin models in two spatial dimensions. We find that the melting of the magnetic long-range order into an isotropic gas-like paramagnet proceeds via an intermediate stage where the classical spins remain anisotropically correlated. This correlated paramagnet exists in a temperature range $T_N <…
Low-temperature magnetization curves and thermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are investigated in a highly frustrated parameter region, where localized many-magnon eigenstates provide the most dominant contribution to magnetothermodynamics. Low-energy states of the highly frustrated spin-1/2 Heisenberg triangular bilayer can be accordingly found from a mapping correspondence with an effective triangular-lattice spin-1/2 Ising model in a field. …
Many-body systems subject to a high-frequency drive can show intriguing thermalization behavior. Prior to heating to a featureless infinite-temperature state, these systems can spend an exponentially long time in prethermal phases characterized by various kinds of order. Here, we uncover the rich non-equilibrium phase diagram of a driven frustrated two-dimensional Ising magnet with competing short-range ferromagnetic and long-range dipolar interactions. We show that the ordered stripe and nematic phases, which appear in equilibrium as a function of temperature, underpin subsequent prethermal p…
Motivated by the recent success of tensor networks to calculate the residual entropy of spin ice and kagome Ising models, we develop a general framework to study frustrated Ising models in terms of infinite tensor networks %, i.e. tensor networks that can be contracted using standard algorithms for infinite systems. This is achieved by reformulating the problem as local rules for configurations on overlapping clusters chosen in such a way that they relieve the frustration, i.e. that the energy can be minimized independently on each cluster. We show that optimizing the choice of clusters, inclu…
Charge correlations in dense ionic fluids give rise to novel effects such as long-range screening and colloidal stabilization which are not predicted by the classic Debye-Huckel theory. We show that a Coulomb or charge-frustrated Ising model, which accounts for both long-range Coulomb and short-range molecular interactions, simply describes some of these ionic correlations. In particular, we obtain at mean field level and in simulations, a non-monotonic dependence of the screening length on the temperature. Using a combination of simulations and mean field theories, we study how the correlatio…
We apply a set of machine-learning (ML) techniques for the global exploration of the phase diagrams of two frustrated 2D Ising models with competing interactions. Based on raw Monte Carlo spin configurations generated for random system parameters, we apply principal-component analysis (PCA) and auto-encoders to achieve dimensionality reduction, followed by clustering using the DBSCAN method and a support-vector machine classifier to construct the transition lines between the distinct phases in both models. The results are in very good agreement with available exact solutions, with the auto-enc…
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…
In this review, we outline the important results on the resistivity encountered by an electron in magnetically ordered materials. The mechanism of the collision between the electron and the lattice spins is shown. Experiments on the spin resistivity in various magnetic materials as well as theoretical background are recalled. We focus on our works since 15 years using principally Monte Carlo simulations. In these works, we have studied the spin resistivity in various kinds of magnetic systems ranging from ferromagnets and antiferromagnets to frustrated spin systems. It is found that the spin r…
By using extensive tensor network calculations, we map out the phase diagram of the frustrated $J_1$-$J_2$ Ising model on the square lattice. In particular, we focus on the cases with controversy in the phase diagram, especially the stripe transition in the regime $g = |J_2/J_1|>\frac{1}{2}$, $(J_2>0,J_1<0)$. While recent studies claimed that the phase transition is of first order when $\frac{1}{2}<g<g^*$ (with the smallest $g^*$ being $0.67$), our simulations suggest that if there is such a first-order region, it is smaller than those found in earlier studies by other methods. Combining with …
We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antifer…
We discuss three exactly solvable spin models of geometric frustration. First, we discuss a 1-parameter subfamily of the 16 vertex model, which can be mapped to a planar Ising model and solved via Fisher-Dubedát decorations. We then consider a 1-parameter family generalization of the Villain's fully frustrated model, which interpolates between Onsager's 2D Ising model and the Villain one. We then discuss spin ice models on a tree, which can be solved exactly using recursions \textit{a lá Bethe}.
Field-tuned order by disorder in Ising frustrated magnets with antiferromagnetic interactions
我们证明了在具有交错反铁磁序的伊辛高温超导体中，在外加磁场的作用下，无序的热有序的出现。我们使用平均场集团变分法、低温展开和蒙特卡罗模拟来模拟有序-无序转变。通过对态密度的直接计算，我们定量地说明了热激发如何选择一个破缺态。我们讨论了我们的研究结果的相关性，在$2d$和$3d$样品的实验，并评估如何异常的有限尺寸效应可以被利用来检测这种现象的实验在二维人工系统中，或在反铁磁的所有在-所有出pyropheres如Nd $_2$铪$_2$ O $_7$或Nd $_2$锆$_2$ O $_7$，为第一次。
