Degenerate ferrimagnetic ground state of frustrated kagome lattice

The frustrated Ising model on kagome lattice with nearest-neighboring antiferromagnetic interaction is investigated by using Monte Carlo simulation of the Wang-Landau algorithm and Glauber dynamics. The geometrical frustration leads to a particularly high degeneracy of ground states in this system. A small magnetic field applied can lift the degeneracy partially, and produce the magnetization plateau of 1/3 saturate value (Ms), which is analogous to the magnetic behavior in triangular antiferromagnetic system. However, different from the long-range ferrimagnetic state responsible for 1/3 Ms plateau in triangular lattice, the ferrimagnetic ground state corresponding to 1/3 Ms plateau in kagome lattice is short-ranged and still highly degenerate. Furthermore, the spin configuration of these degenerate ferrimagnetic ground states show an inherent characteristic that the spins along the magnetic field must be aligned on the closed loops, which can be well understood in terms of geometrical frustration.     

Partially disordered antiferromagnetic state in two-dimensional triangular-lattice antiferromagnet

The partially disordered antiferromagnetic (PDA) state, as an exotic phase peculiar to the antiferromagnet with Ising spin in triangular lattice, is investigated by using Monte Carlo simulations of Wang-Landau algorithm and Glauber algorithm. It is revealed that PDA state, as the ground state of the triangular antiferromagnetic system, presents the complicated spin configuration due to geometrical frustration. The formation of multi-domain structure within the framework of honeycomb antiferromagnet results in the high degeneracy of PDA state. And this degeneracy of ground state can be lifted by a small magnetic field. Consequently the system shows the ferrimagnetic state, and the magnetization plateau of 1/3 saturate value (Ms) is observed in many experiments. Moreover, due to the multi-domain structure of PDA state and those spins on domain walls, the metastable steps may manifest themselves superposed on the 1/3Ms plateau in some special cases.     

Boundary energy and boundary states in integrable quantum field theories

We study the ground-state energy of integrable 1 + 1 quantum field theories with boundaries (the genuine Casimir effect). In the scalar case, this is done by introducing a new “R-channel TBA”, where the boundary is represented by a boundary state, and the thermodynamics involves evaluating scalar products of boundary states with all the states of the theory. In the non-scalar, sine-Gordon case, this is done by generalizing the method of Destri and De Vega. The two approaches are compared. Miscellaneous other results are obtained, in particular formulas for the overall normalization and scalar products of boundary states, exact partition functions for the critical Ising model in a boundary magnetic field, and also results for the energy, excited states and boundary S-matrix of O(n) and minimal models.     

EPR spectra of the excited nitrogen state in 6H-SiC

A study is reported of donor EPR spectra in compensated 6H-SiC crystals with donor concentrations (N _D -N _A ) varied from 8×10¹⁷ to 5×10¹⁶ cm^?3, performed within a temperature interval from 77 to 170 K at a frequency of 37 GHz. A second paramagnetic state of nitrogen in silicon carbide has been found to exist, and it is associated with its excited 1S(E) state becoming paramagnetic after thermal ionization of the donor electrons from the 1S(A ₁) to 1S(E) level. The EPR spectrum of nitrogen in the 1S(E) state is a single line with an anisotropic width because of the unresolved hyperfine structure. A light-induced charge transfer between the ground, 1S(A ₁), and excited, 1S(E), nitrogen states has been observed. The valley-orbit splitting and the energy required to ionize donor electrons from the 1S(E) to higher lying excited states have been determined for the cubic nitrogen sites. The parameters of a structural defect, characteristic of n-type 6H-SiC compensated crystals, have been established.     

Optical oscillator strengths for Be II and B III

A simple two-parameter analytic potential adjusted so as to produce the experimental energy levels is used to generate wave functions for the ground and excited states of the ions Be II and B III. Using these wave functions we calculate optical oscillator strengths for various excitations from the 1s ²2s(² S) ground state. The results are compared to experiment and other calculations.     

Stabilization of a steady state in oscillators coupled by a digital delayed connection

We propose the mapping of polynomial of degree 2S constructed as a linear combination of powers of spin-S (for simplicity, we called as spin-S polynomial) onto spin-crossover state. The spin-S polynomial in general can be projected onto non-symmetric degenerated spin up (high-spin) and spin down (low-spin) momenta. The total number of mapping for each general spin-S is given by 2(2^2S ? 1). As an application of this mapping, we consider a general non-bilinear spin-S Ising model which can be transformed onto spin-crossover described by Wajnflasz model. Using a further transformation we obtain the partition function of the effective spin-1/2 Ising model, making a suitable mapping the non-symmetric contribution leads us to a spin-1/2 Ising model with a fixed external magnetic field, which in general cannot be solved exactly. However, for a particular case of non-bilinear spin-S Ising model could become equivalent to an exactly solvable Ising model. The transformed Ising model exhibits a residual entropy, then it should be understood also as a frustrated spin model, due to competing parameters coupling of the non-bilinear spin-S Ising model.     

Real space renormalization group approach to the two-dimensional antiferromagnetic Heisenberg model (I) – The singlet triplet gap

The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix Δ_S ⁽ⁿ⁺¹⁾ of 4 neighbouring “n clusters” of size 2ⁿ × 2ⁿ, n = 1,2,3,... from the corresponding quantities Δ_S ⁽ⁿ⁾. Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies E_S ⁽ⁿ⁺¹⁾, S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions 〈S’,m’;n+1|S_q ^*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2ⁿ⁺¹ × 2ⁿ⁺¹, mediated by the staggered spin operator S_q ^*.     

Haldane gap in a S=1 exchange model with long-range interactions

The ground-state properties of the S = 1 Haldane- Shastry model are studied using a modified Lanczos algorithm and diagonalizing exactly small chains. We find evidence that, as for the antiferromagnetic Heisenberg model, the spectrum shows a gap, in contrast to the {ie1-1} case. The correlation functions < S ^z(0)S ^z(m) > decay exponentially for large m. We find that the correlation functions for the Haldane-Shastry model decay faster than for the Heisenberg model. We estimate the infinite system limit for the groundstate energy, value of the gap and correlation functions.     

Trajectory of neutron–neutron–C excited three-body state

The trajectory of the first excited Efimov state is investigated by using a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems. The approach is applied to n–n–¹⁸C, where the n–n$n\text{–}n$ virtual energy and the three-body ground state are kept fixed. It is shown that such three-body excited state goes from a bound to a virtual state when the n–¹⁸C binding energy is increased. Results obtained for the n–¹⁹C elastic cross-section at low energies also show dominance of an S-matrix pole corresponding to a bound or virtual Efimov state. It is also presented a brief discussion of these findings in the context of ultracold atom physics with tunable scattering lengths.     

A low-lying resonance in the spectrum of H

It was proved by Pekeris⁽¹⁾ that the singly excited states of H^- lie exactly at, or slightly above, the ground state of hydrogen. Using a theory of Fano,⁽²⁾ these fictitious states will have a configuration interaction with the H^- continuum. The strength of this configuration interaction is computed for the mixing of a 1s2p¹P⁰ state with the H^- continuum for different values of the fictitious binding energy of the 2p valence electron. In every case, the effect of the configuration interaction is to induce a rapid change of the phase shift of the continuum wave function by a quantity of π/2 over an energy range of a few times 0.01 eV, at an energy somewhat above the hydrogen ground state. The variation from π/2 to π is much slower. Such a swift change of the phase shift may be identified with the occurrence of a low-lying shape resonance.     

Formation of Stripes and Slabs Near the Ferromagnetic Transition

We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance)^?p , p > 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value J _c , then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to J _c , the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as \({J\to J_c^-}\) . (In d = 3 stripes mean slabs, not columns.) Here we rigorously prove that, if we normalize the energy in such a way that the energy of the homogeneous state is zero, then the ratio e ₀(J)/e _S(J) tends to 1 as \({J\to J_c^-}\) , with e _S(J) being the energy per site of the optimal periodic striped/slabbed state and e ₀(J) the actual ground state energy per site of the system. Our proof comes with explicit bounds on the difference e ₀(J)?e _S(J) at small but positive J _c ?J, and also shows that in this parameter range the ground state is striped/slabbed in a certain sense: namely, if one looks at a randomly chosen window, of suitable size ? (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed state with high probability.     

Fe2+ localized excitations in the random antiferromagnet with competing spin anisotropies, Fe(1−x)CoxBr2

The Fe²⁺ localized magnetic excitations observed in the Co-rich antiferromagnetic phase of the randomly mixed system with competing Ising and XY spin anisotropies, Fe(_1?x)Co_xBr₂ have been analyzed quantitatively. The calculated frequency-field diagram reproduces well the experiments. The expectation values of the Fe²⁺ spin components in the ground state are calculated. It is shown that even in the Co-rich antiferromagnetic phase Fe²⁺ spins make an angle with the c-plane of the crystal in which Co²⁺ spins are confined.     

Thermodynamics of the quantum and classical Ising models with skew magnetic field

The thermodynamics of the unitary (normalized spin) quantum and classical Ising models with skew magnetic field, for |J|β?0.9, is derived for the ferromagnetic and antiferromagnetic cases. The high-temperature expansion (β-expansion) of the Helmholtz free energy is calculated up to order β⁷ for the quantum version (spin S≥1/2) and up to order β¹⁹ for the classical version. In contrast to the S=1/2 case, the thermodynamics of the transverse Ising and that of the XY model for S>1/2 are not equivalent. Moreover, the critical line of the T=0 classical antiferromagnetic Ising model with skew magnetic field is absent from this classical model, at least in the temperature range of |J|β?0.9.     

The ground state and its entropy for a class of one-dimensional classical lattice systems

We calculate explicitly the zero-temperature limit of the finite temperature equilibrium state and its entropy for a class of one-dimensional Ising models with an interaction of range n. For that purpose we extend the usual transfer matrix method to ground states. The interaction consists of a ferromagnetic nearest neighbour term and a competing antiferromagnetic interaction with the nth neighbour.     

Deconfinement phase transition in a two-dimensional model of interacting 2 × 2 plaquettes

The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix Δ_S ⁽ⁿ⁺¹⁾ of 4 neighbouring “n clusters” of size 2ⁿ × 2ⁿ, n = 1,2,3,... from the corresponding quantities Δ_S ⁽ⁿ⁾. Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies E_S ⁽ⁿ⁺¹⁾, S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions 〈S’,m’;n+1|S_q ^*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2ⁿ⁺¹ × 2ⁿ⁺¹, mediated by the staggered spin operator S_q ^*.     

Low-lying excitations in the S = 1 antiferromagnetic Heisenberg chain

In order to confirm the picture of domain-wall excitations in the hidden antiferromagnetic order of the Haldane phase, the structure of the low-lying excitations in the S = 1 antiferromagnetic Heisenberg chain is studied by a quantum Monte Carlo method. It is confirmed that there exists a finite energy gap between the first- and the second-excited states at k = π as well as between the ground state and the first-excited state at k = π. In the thermodynamic limit, the second-excited state at k = π is separated from the ground state by the gap which is three times as large as the Haldane gap. From the size dependences of the low-lying-excitation energies, the interactions between the elementary excitations in the excited states are concluded to be repulsive.     

Exactly solvable model of a spin glass

Sherrington and Kirkpatrick presented a solvable model of a spin glass. In the solution, they used a mathematically unwarranted procedure. In the present article, we show that the problem is exactly solved by starting with the virial expansion formula, and confirm the results of Sherrington and Kirkpatrick. The solution is obtained for the random Ising magnet in which the external field of each site and the exchange integral between each pair of sites are random variables. We obtain the exact thermodynamic properties for this system in the limit of n_w→∞, assuming that the exchange integrals of a spin with O(n_w) neighbours are $\text{O(n}{}_{\mathrm{w}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{)}$ and the average value of each is O(n_w^?1). The system is found to show the spin-glass state as well as the paramagnetic and the ferromagnetic state.     

Antiferromagnetic phase transition in garnet-type AgCa2Co2V3O12 and AgCa2Ni2V3O12

Antiferromagnetic phase transition in two vanadium garnets AgCa₂Co₂V₃O₁₂ and AgCa₂Ni₂V₃O₁₂ has been found and investigated extensively. The heat capacity exhibits sharp peak due to the antiferromagnetic order with the Néel temperature T_N=6.39 K for AgCa₂Co₂V₃O₁₂ and 7.21 K for AgCa₂Ni₂V₃O₁₂, respectively. The magnetic susceptibilities exhibit broad maximum, and these T_N correspond to the inflection points of the magnetic susceptibility χ a little lower than T(χ_max). The magnetic entropy changes from zero to 20 K per mol Co²⁺ and Ni²⁺ ions are 5.31 J K⁻¹ mol-Co²⁺-ion⁻¹ and 6.85 J K⁻¹ mol-Ni²⁺-ion⁻¹, indicating S=1/2 for Co²⁺ ion and S=1 for Ni²⁺ ion. The magnetic susceptibility of AgCa₂Ni₂V₃O₁₂ shows the Curie-Weiss behavior between 20 and 350 K with the effective magnetic moment μ_eff=3.23 μ_B Ni²⁺-ion⁻¹ and the Weiss constant θ=−16.4 K (antiferromagnetic sign). Nevertheless, the simple Curie-Weiss law cannot be applicable for AgCa₂Co₂V₃O₁₂. The complex temperature dependence of magnetic susceptibility has been interpreted within the framework of Tanabe-Sugano energy diagram, which is analyzed on the basis of crystalline electric field. The ground state is the spin doublet state ²E(t₂⁶e) and the first excited state is spin quartet state ⁴T₁(t₂⁵e²) which locates extremely close to the ground state. The low spin state S=1/2 for Co²⁺ ion is verified experimentally at least below 20 K which is in agreement with the result of the heat capacity.     

Phase diagrams of the Ising-Heisenberg chain with S = 1/2 triangular XXZ clusters

The one-dimensional spin system consisted of triangular S = 1/2 XXZ Heisenberg clusters alternating with single Ising spins is considered. Partition function of the system is calculated exactly within the transfer-matrix formalism. T = 0 ground state phase diagrams, corresponding to different regions of the values of system parameters, are obtained.     

Phase Diagram and Structure of the Ground State of the Antiferromagnetic Ising Model on a Body-Centered Cubic Lattice

The Monte Carlo method has been used to study phase transitions and the structure of the ground state of the antiferromagnetic Ising model on a body-centered cubic lattice taking into account the interactions of nearest and next nearest neighbors. All possible magnetic structures of the ground state have been obtained for the first time as a function of the ratio of exchange interactions r. It is shown that six different orderings in the ground state are possible in the system as a function of the r value. The phase diagram of the dependence of the critical temperature on the interaction of the next nearest neighbors is constructed. For the first time, a narrow region (2/3 < r ≤ 0.75) is found in the diagram where the transition from the antiferromagnetic phase to the paramagnetic phase occurs as a first-order phase transition. It is shown that the competition between exchange interactions at the value r = 2/3 does not lead to the frustration and degeneracy of the ground state.