Ferroelectricity in an ising chain magnet

We report discovery of collinear-magnetism-driven ferroelectricity in the Ising chain magnet Ca3Co2-xMn(x)O6 (x approximately 0.96). Neutron diffraction shows that Co2+ and Mn4+ ions alternating along the chains exhibit an up-up-down-down ( upward arrow upward arrow downward arrow downward arrow) magnetic order. The ferroelectricity results from the inversion symmetry breaking in the upward arrow upward arrow downward arrow downward arrow spin chain with an alternating charge order. Unlike in spiral magnetoelectrics where antisymmetric exchange coupling is active, the symmetry breaking in Ca3(Co,Mn)2O6 occurs through exchange striction associated with symmetric superexchange.     

Absence of a spontaneous long-range order in a mixed spin-(1/2, 3/2) Ising model on a decorated square lattice due to anomalous spin frustration driven by a magnetoelastic coupling

The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which takes into account lattice vibrations of the spin-3/2 decorating magnetic ions at a quantum-mechanical level under the assumption of a perfect lattice rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping correspondence with the effective spin-1/2 Ising model on a square lattice. Although the considered magnetic structure is in principle unfrustrated due to bipartite nature of a decorated square lattice, the model under investigation may display anomalous spin frustration driven by a magnetoelastic coupling. It turns out that the magnetoelastic coupling is a primary cause for existence of the frustrated antiferromagnetic phases, which exhibit a peculiar coexistence of antiferromagnetic long-range order of the nodal spins with a partial disorder of the decorating spins with possible reentrant critical behavior. Under certain conditions, the anomalous spin frustration caused by the magnetoelastic coupling is responsible for unprecedented absence of spontaneous long-range order in the mixed-spin Ising model composed from half-odd-integer spins only.     

Duality Between Spin Networks and the 2D Ising Model

The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.     

Critical and multicritical behavior in the Ising–Heisenberg universality class

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang–Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N = 1, 2, 3 and in all of them find a first-order transition. For the N = 1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.     

Long-range order at low temperatures in dipolar spin ice

It has recently been suggested that long-range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets Dy2Ti2O7 and Ho2Ti2O7. We report here numerical results on the low temperature properties of the dipolar spin ice model, obtained via a new loop algorithm which greatly improves the dynamics at low temperature. We recover the previously reported missing entropy in this model, and find a first order transition to a long-range ordered phase with zero total magnetization at very low temperature. We discuss the relevance of these results to Dy2Ti2O7 and Ho2Ti2O7.     

Efficient algorithm for random-bond ising models in 2D

We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm computes the partition function and correlation functions at a single temperature on any planar network of N Ising spins in O(N;{3/2}) time or less. The method can handle continuous or discrete bond disorder and is especially efficient in the case of bond or site dilution, where it executes in O(NlnN) time near the percolation threshold. We demonstrate its feasibility on the ferromagnetic Ising model and the +/-J random-bond Ising model and discuss the regime of applicability in cases of full frustration such as the Ising antiferromagnet on a triangular lattice.     

Phase Transitions of a Dilute O(n) Model

We investigate tricritical behavior of the O(n) model in two dimensions by means of transfer-matrix and finite-size scaling methods. For this purpose we consider an O(n) symmetric spin model on the honeycomb lattice with vacancies; the tricritical behavior is associated with the percolation threshold of the vacancies. The vacancies are represented by face variables on the elementary hexagons of the lattice. We apply a mapping of the spin degrees of freedom model on a non-intersecting-loop model, in which the number n of spin components assumes the role of a continuously variable parameter. This loop model serves as a suitable basis for the construction of the transfer matrix. Our results reveal the existence of a tricritical line, parametrized by n, which connects the known universality classes of the tricritical Ising model and the theta point describing the collapse of a polymer. On the other side of the Ising point, the tricritical line extends to the n=2 point describing a tricritical O(2) model.     

Local entropy and structure in a two-dimensional frustrated system

We calculate the local contributions to the Shannon entropy and excess entropy and use these information theoretic measures as quantitative probes of the order arising from quenched disorder in the diluted Ising antiferromagnet on a triangular lattice. When one sublattice is sufficiently diluted, the system undergoes a temperature-driven phase transition, with the other two sublattices developing magnetizations of equal magnitude and opposite sign as the system is cooled.(1) The diluted sublattice has no net magnetization but exhibits spin glass ordering. The distribution of local entropies shows a dramatic broadening at low temperatures; this indicates that the system's total entropy is not shared equally across the lattice. The entropy contributions from some regions exhibit local reentrance, although the entropy of the system decreases monotonically as expected. The average excess entropy shows a sharp peak at the critical temperature, showing that the excess entropy is sensitive to the structural changes that occur as a result of the spin glass ordering.     

Order-from-disorder effect in the exactly solved mixed spin-(1/2, 1) Ising model on fully frustrated triangles-in-triangles lattices

The mixed spin-(1/2, 1) Ising model on two fully frustrated triangles-in-triangles lattices is exactly solved with the help of the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the equivalent spin- 1/2 Ising model on a triangular lattice. It is shown that the mutual interplay between the spin frustration and single-ion anisotropy gives rise to various spontaneously ordered and disordered ground states, which differ mainly in an occurrence probability of the non-magnetic spin state of the integer-valued decorating spins. We have convincingly evidenced a possible coexistence of the spontaneous long-range order with a partial disorder within the striking ordered–disordered ground state, which manifests itself through a non-trivial criticality at finite temperatures as well. A rather rich critical behavior including the order-from-disorder effect and reentrant phase transitions with either two or three successive critical points is also found.     

一种推广伊辛自旋模型的实空间重正化群理论

本文提出了一种推广的伊辛自旋模型。它包括了伊辛自旋模型、Schofield和Bowers提出的混合自旋模型以及一种特殊的格点稀释伊辛自旋模型作为特例。运用实空间重正化群得到了这个推广模型的相变流图和三个非平庸不动点(一个伊辛不动点,一个三相不动点和一个一级相变不动点)。结果表明:混合自旋模型和伊辛模型属于同一普适类。证实了Schofield和Bowers通过直接对混合自旋模型临界指数的计算所做的结论。 关键词：     

Dipolar interactions and origin of spin ice in ising pyrochlore magnets

Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the nearest-neighbor "spin ice" model. We discuss the dipolar energy scale present in both these materials and discuss how spin-ice behavior can occur despite the presence of long-range dipolar interactions. We present results of numerical simulations and a mean field analysis of Ising pyrochlore systems. Based on our quantitative theory, we suggest that the spin-ice behavior in these systems is due to long-range dipolar interactions, and that the nearest-neighbor exchange in Dy2Ti2O7 is antiferromagnetic.     

Exact ground state of a spin ladder with a quantum phase transition

We introduce a spin ladder with Ising interactions along the legs and intrinsically frustrated Heisenberg-like ferromagnetic interactions on the rungs. The model is solved exactly in the subspaces relevant for the ground state by mapping to the quantum Ising model, and we show that a first order quantum phase transition separates the classical from quantum regime, with the spin correlations on the rungs being either ferromagnetic or antiferromagnetic, and different spin excitations in both regimes. The present case resembles the quantum phase transition found in the compass model in one and two dimensions.     

Order by disorder and gaugelike degeneracy in a quantum pyrochlore antiferromagnet

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length S is a highly frustrated model with a macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic-order) spin-wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating effective Hamiltonian, acting within the subspace of Ising spin configurations representing the collinear ground states. It consists of products of Ising spins around loops, i.e., has the form of a Z2 lattice gauge theory. The remaining ground-state entropy is still infinite but not extensive, being O(L) for system size O(L3). All these ground states have unit cells bigger than those considered previously.     

一维自旋-轨道模型中的畴状轨道液体态

研究了一个一维可解自旋-轨道模型.在大自旋极限下，自旋自由度可以近似用经典自旋来描 述.在没有外磁场情形，系统的基态是伊辛自旋反铁磁背景下的轨道液体态.其低能元激发是 类似于spinon的轨道量子.而在有外磁场情形，系统会出现磁通点阵相.同时，磁通将系统分 割成不连通的轨道液体. 关键词： 自旋轨道系统 畴状轨道液体     

Amide proton relaxation measurements employing a highly deuterated protein

Proton NMR longitudinal and transverse relaxation rates of unlabelled proteins are generally dominated by the many 1H-1H dipolar interactions so that spin diffusion, rather than molecular or internal motions, governs longitudinal relaxation. Here, relaxation measurements of backbone amide proton (1H(N)) magnetisations have been carried out employing the 99% 2H, 98% 15N labelled, small 2F2 protein domain in 10%/90% H(2)O/D(2)O solution. Under these conditions, the longitudinal relaxation rates exhibit time constants, T(1)*=1/R(1)* if described by a mono-exponential, within the range of 3.0 to 18.7s-a wide range which indicates that the phenomenon of spin diffusion has been greatly reduced. The majority of 1H(N) nuclei in this sample (pH 4.0 and 5 degrees C) exhibit chemical exchange with solvent that couples their longitudinal relaxation to that of the solvent. For the subset of 1H(N) nuclei not undergoing detectable solvent chemical exchange, the R(1)* rates correlate well with their individual 1H(N,O)/2H(N,O) structural environments. The correlation for corresponding transverse relaxation rates, R(2)* was found to be less good. Longitudinal relaxation measurements in 1%/99% H(2)O/D(2)O solution identify a further subset of 1H(N) nuclei which exhibit essentially indistinguishable R(1)* rates in both 1% and 10% H(2)O, implying that averaging of rates from spin diffusion processes and different 2F2 isotopomer populations are negligible for these 1H(N) sites. In addition to a high sensitivity to structural parameters, model calculations predict 1H(N) relaxation rates to exhibit pronounced sensitivity to internal dynamics.     

Slow magnetic order-order transition in the spin chain antiferromagnet Ca3Co2O6

Using powder neutron diffraction, we have discovered an unusual magnetic order-order transition in the Ising spin chain compound Ca3Co2O6. On lowering the temperature, an antiferromagnetic phase with a propagation vector k=(0.5,-0.5,1) emerges from a higher temperature spin density wave structure with k=(0,0,1.01). This transition occurs over an unprecedented time scale of several hours and is never complete.     

Microcanonical relation between continuous and discrete spin models

A relation between a class of stationary points of the energy landscape of continuous spin models on a lattice and the configurations of an Ising model defined on the same lattice suggests an approximate expression for the microcanonical density of states. Based on this approximation we conjecture that if a O(n) model with ferromagnetic interactions on a lattice has a phase transition, its critical energy density is equal to that of the n=1 case, i.e., an Ising system with the same interactions. The conjecture holds true in the case of long-range interactions. For nearest-neighbor interactions, numerical results are consistent with the conjecture for n=2 and n=3 in three dimensions. For n=2 in two dimensions (XY model) the conjecture yields a prediction for the critical energy of the Bere?inskij-Kosterlitz-Thouless transition, which would be equal to that of the two-dimensional Ising model. We discuss available numerical data in this respect.     

Generalized transformation for decorated spin models

The paper discusses the transformation of decorated Ising models into an effective undecorated spin model, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes [−s,s] is used to obtain an analytical expression of the transformation. This kind of transformation is very useful to obtain the partition function of decorated systems. The method presented by Fisher is also extended, in order to obtain the correlation functions of the decorated Ising models transforming into an effective undecorated Ising model. We apply this transformation to a particular mixed spin-(1/2, 1) and (1/2, 2) square lattice with only nearest site interaction. This model could be transformed into an effective uniform spin-S square lattice with nearest and next-nearest interaction, furthermore the effective Hamiltonian also includes combinations of three-body and four-body interactions; in particular we considered spin 1 and 2.     

Direct determination of the magnetic structure of the delta phase of oxygen

Simple diatomic molecules exhibit a variety of exciting physical phenomena under high pressures, including structural transitions, pressure induced metallization, and superconductivity. Oxygen is of particular interest because it carries a magnetic moment. For the first time we studied the magnetic structure in solid oxygen under very high pressure by a direct method, namely, neutron diffraction. A new type of magnetic order with ferromagnetic stacking of the antiferromagnetic O2 planes was discovered in delta-O2 at P=6.2 GPa. We show that all structural transformations at pressures <7 GPa are driven by spin interactions; therefore, high-pressure oxygen should be considered as a unique "spin-controlled crystal."     

Magnetic properties of 1d systems with a subtle stacking of copper(II) ions

In the last two decades, many studies have been reported on infinite Id networks of magnetically interacting metal ions. Until now, closed-form expressions for the partition function and related properties were mainly derived for the S = f Ising chain model (Ising, 1925), the XY model (Kastura, 1962) or for the classical limit S –t co with arbitrary spin dimensionality (Fischer, 1964). Recently, experimental and theoretical studies have focused on new Id systems made of alternating spin and/or Lande factors (Georges, Curely and Drillon, 1985; Drillon et al., 1983). This has motivated our interest in the behavior of new systems of copper(II) ions in which the magnetic sites form an exotic stacking in one direction of the crystal. Then, the specific behavior is related to the competition between different interactions, as occurs in the systems reported here, namely A₃Cu₃(PO₄)₄, with A = Ca, Sr, Cu₃(PO₄)₂ and Cu₂O(SO₄).