Entanglement in (1/2,1) Mixed-Spin XY Model with Long-Range Interaction

In this study, we investigate entanglement in a two mixed-spin (1/2,1) XY Heisenberg spin system under an applied magnetic field by considering the long-range interaction with an inverse-square function. The spin-spin coupling constant is considered as a function of the distance between spins. We also discuss the temperature and magnetic field dependence of the thermal entanglement in this system for this interaction. The numerical results show that, in the presence of the long-range interaction, thermal entanglement between spins has a rich behavior dependent upon the interaction strength, temperature and magnetic field. We find that for less than a critical distance there are entanglement plateaus dependent upon the distance between spins, whereas above the critical distance the entanglement can exhibit sudden death.     

Thermal entanglement in the mixed three-spin XXZ Heisenberg model on a triangular cell

We numerically investigate the thermal entanglements of spins （1/2, 1） and spins （1/2, 1/2） in the three-mixed （1/2, 1, 1/2） anisotropic Heisenberg XXZ spin system on a simple triangular cell under an inhomogeneous magnetic field. We show that the external magnetic field induces strong plateau formation in the pairwise thermal entanglement for fixed parame-ters of the Hamiltonian in the cases of ferromagnetic and antiferromagnetic interactions. We also .observe an unexpected critical point at finite temperature in the thermal entanglement of spins （1/2, 1） for the antiferromagnetic case, while the entanglement of spins （1/2, 1） in the ferromagnetic case and the entanglement of spins （1/2, 1/2） in both ferromagnetic and antiferromagnetic cases almost decay exponentially to zero with increasing temperature. The critical point in the en-tanglement of spins （1/2, 1） in the antiferromagnetic case may be a signature of the quantum phase transition at finite temperature.     

A new method for calculation of the magnetic properties in one- and two-dimensional spin systems with anisotropic Heisenberg exchange

A new approximation method is proposed for the calculation of the magnetic susceptibility of one-dimensional assembly of spins and the critical temperature of two-dimensional one both with the anisotropic Heisenberg exchange. In a linear chain system, every spins are grouped into pairs of adjacent spins (pair-approximation) or clusters of adjacent three spins ((q+1)-approximation), and the partition function of the total spin system is approximated as a sum of products of the partitions functions for the pairs or the clusters. Then the partition function of the anisotropic Heisenberg spin system is shown to reduce into a form of the Ising spin system with modified coupling constants. The exact result for the Ising chain system enables us to obtain an analytical expression for the magnetic susceptibility of anisotropic Heisenberg chain system. The same approximations are also applied to two-dimensional lattices, and the critical temperatures of the square, triangular, and honeycomb lattices with anisotropic Heisenberg exchange are calculated as a function of anisotropy parameter. The results are compared with those of the existing theories and shown to be quite excellent.     

Planar spin system with annealed bond disorder

This is a study of the equilibrium statistical mechanics of a mixed system of planar spins and Ising spins. The Ising spins σ_r are situated (one on each of the bonds connecting the planar spins s_r so that the planar spins interact only via Ising spins. For a one-dimensional lattice the partition function and the two-spin correlation functions (σ_rσ_r¹ and S_r·S_r¹) are calculated ex actly in terms of modified Bessel functions.

For a two-dimensional anisotropic generalization of the model an equation is given for the critical temperature and the equation is shown to have one and only one solution T_c such that 0<T_c<∞.     

自旋S=1座稀释蜂窝格子的伊辛模型

本文对于自旋S=1的淬灭座稀释蜂窝格子的伊辛模型,在约束条件exp(K)cosh(J)=1下,求得了系统的临界温度和磁化强度与自旋浓度之间的关系。 关键词：     

Spin correlations in 2 + ε dimensions - ordered and disordered phase

Closed form expressions for the correlation functions of fixed length spins in 2 and 2 + ? dimensions below and above the critical temperature are obtained by a skeleton graph approach.     

Mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice within the effective-field theory

An effective-field theory with correlations is developed for a mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice. Spin-1 atoms and spin-3/2 atoms are distributed in alternative layers of a honeycomb lattice. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the interaction between the vertically aligned spins and adjacent spins are coupled either ferromagnetically or antiferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the temperature dependence of the total magnetization to find the compensation points and to determine the type of compensation behavior. We present the phase diagrams in different planes for h=0, and the phase diagrams contain the paramagnetic, nonmagnetic and ferrimagnetic phases. The system also presents a tricritical behavior besides multicritical point (A), isolated critical point (C) and double critical end point (B) depending on the interaction parameters.     

Analysis of the migdal transformation for models with Heisenberg spins on a d-dimensional lattice

We show for classical Heisenberg spins, with a general nearest neighbour interaction, that in the Migdal approximation the only low-temperature phase transitions are Ising ones (ferror antiferromagnetic). For d=2 neither the pure Heisenberg model nor the Lebwohl-Lasher model show a phase transition at a finite temperature. For d>2 transitions do exist at intermediate temperature and the complete flow diagram together with a two-parameter phase diagram is obtained numerically for d=3. Apart from critical temperatures and thermal exponents, also the magnetic exponents (for both Heisenberg and XY spins) are calculated. The latter are in very good agreement with exact results.     

Nucleation theorems applied to the Ising model

We use Monte Carlo simulations to study a single cluster of "up" spins in a sea of "down" spins in the three-dimensional Ising model. We evaluate the growth and decay rates for clusters of different sizes, identify the critical size for which these rates are equal, and obtain the internal energy of the critical size cluster. The results of the simulations at different temperatures and magnetic fields are used together with the first and second nucleation theorems to predict how the cluster nucleation rate changes when the external magnetic field and the temperature are changed. Our results are in agreement with literature values, but our method requires significantly less computational effort than the simulations reported earlier and avoids the difficult evaluation of free energies.     

Two-dimensional small particles coupled by dipolar interactions

We study the effect of the dipolar coupling on the magnetic properties of two small interacting ferromagnetic particles. Each particle is a two-dimensional array of Ising spins with a central spin surrounded by a variable number of shells. The coupling between spins inside each particle is ferromagnetic and the dipolar interaction between the particles is determined as a function of the number of shells, temperature, and distance between their centers. We investigate the system by mean-field approximation and Monte Carlo simulations. The dipolar interaction is calculated in two ways, one assuming effective spins in the centers of the particles, and the other directly computing the interactions among all the pairs of spins, one in each particle. We show that the difference in the corresponding dipolar energies is a power law on the distance with exponent 5. We calculate the magnetization and susceptibility as a function of temperature, number of shells and distance between the particles’ centers. We show that the critical temperature increases with the number of spins in each particle, and it is more noticeable in the mean-field calculations than in the Monte Carlo simulations.     

Limit probability distributions for an infinite-order phase transition model

The limiting probability distributions for the one-dimensional inhomogeneous spin system considered in a previous paper, which exhibits an infinite-order phase transition, are computed. It turns out that below the critical temperature or in the presence of an external magnetic field, the spins are completely polarized.     

Point defects in the honeycomb Ising lattice

A plane isotropic honeycomb Ising lattice is considered with randomly distributed defects, namely missing lattice spins (including the three adjacent bonds). The impurities are in thermodynamic equilibrium through a chemical potential. We find a rescaled temperature and a finite cusp-like specific heat at the critical point.     

Antiferromagnetism of nuclear matter in the model with effective Gogny interaction

The possibility of ferromagnetic (FM) and antiferromagnetic (AFM) phase transitions in symmetric nuclear matter is analyzed within the framework of a Fermi liquid theory with effective Gogny interaction. It is shown that, at some critical density, nuclear matter with the D1S effective force undergoes a phase transition to the AFM spin state (opposite directions of neutron and proton spins). The self-consistent equations of spin-polarized nuclear matter with the D1S force have no solutions corresponding to FM spin ordering (the same direction of neutron and proton spins) and, hence, the FM transition does not appear. The AFM spin polarization parameter is found for zero and finite temperature. It is shown that the AFM spin polarization parameter of partially polarized nuclear matter at low enough temperatures increases with temperature. The entropy of the AFM spin state for some temperature range is larger than the entropy of the normal state. Nevertheless, the free energy of the AFM spin state is always less than the free energy of the normal state, and the AFM spin-polarized state is preferable for all temperatures below the critical temperature. The text was submitted by the authors in English.     

Surface-induced ordering in thin uniaxial liquid crystal films

The interface localization transition in thin uniaxial liquid crystal films with competing surface fields has been studied using Metropolis Monte Carlo simulations. The model is constructed from a lattice of continuously orientable interacting spins, and the Hamiltonian contains both bilinear and biquadratic contributions. The biquadratic contribution to the Hamiltonian is familiar from the Lebwohl-Lasher model, and accounts for the particle anisotropy in a liquid crystal. The head-tail asymmetry of the molecules in a uniaxial liquid crystal is taken into account through a bilinear contribution familiar from the classical ferromagnetic Heisenberg model with exchange anisotropy Lambda. The critical temperature T(c), characterizing the interface localization transition within the uniaxial liquid crystal film, depends strongly on the relative magnitudes of the bilinear and biquadratic interactions between the spins. For systems dominated by the biquadratic interaction, T(c) is found to be close to the bulk critical temperature of the system. But as the biquadratic interaction strength is reduced, T(c) departs markedly from the bulk critical temperature of the system.     

Ising Models with Four Spin Interaction at Criticality

We consider two bidimensional Ising models coupled by an interaction quartic in the spins, like in the spin representation of the Eight vertex or the Ashkin-Teller model. By Renormalization Group methods we write a convergent perturbative expansion for the specific heat and for the energy-energy correlation up to the critical temperature. A form of nonuniversality is proved, in the sense that the critical behaviour is described in terms of critical indices which are non trivial functions of the coupling. The logarithmic singularity of the specific heat of the Ising model is removed or changed in a power law (with a non universal critical index) depending on the sign of the interaction.     

Critical droplets and metastability for a Glauber dynamics at very low temperatures

We consider the metastable behavior in the so-called pathwise approach of a ferromagnetic spin system with a Glauber dynamics in a finite two dimensional torus under a positive magnetic field in the limit as the temperature goes to zero. First we consider the evolution starting from a single rectangular droplet of spins +1 in a sea of spins −1. We show that small droplets are likely to disappear while large droplets are likely to grow; the threshold between the two cases being sharply defined and depending only on the external field. This result is used to prove that starting from the configuration with all spins down (−1) the pattern of evolution leading to the more stable configuration with all spins up (+1) approaches, as the temperature vanishes, a metastable behavior: the system stays close to −1 for an unpredictable time until a critical square droplet of a precise size is eventually formed and nucleates the decay to +1 in a relatively short time. The asymptotic magnitude of the total decay time is shown to be related to the height of an energy barrier, as expected from heuristic and mean field studies of metastability. Partially supported by CNPq. Part of this work was done while RHS was visiting Rome, supported by an agreement between CNPq and CNR     

Compensation temperature of 3d mixed ferro-ferrimagnetic ternary alloy

In this study, we have considered the three dimensional mixed ferro-ferrimagnetic ternary alloy model of the type AB_pC_1-p where the A and X (X=B or C) ions are alternately connected and have different Ising spins S^A=3/2, S^B=1 and S^C=5/2, respectively. We have investigated the dependence of the critical and compensation temperatures of the model on concentration and interaction parameters by using MC simulation method. We have shown that the behavior of the critical temperature and the existence of compensation points strongly depend on interaction and concentration parameters. In particular, we have found that the critical temperature of the model is independent on concentration of different types of spins at a special interaction value and the model has one or two compensation temperature points in a certain range of values of the concentration of the different spins.     

Bipartite entanglement in the spin-1/2 Ising-Heisenberg planar lattice constituted of identical trigonal bipyramidal plaquettes

The bipartite entanglement is rigorously examined in the spin-1/2 Ising-Heisenberg planar lattice composed of identical inter-connected bipyramidal plaquettes at zero and finite temperatures using the quantity called concurrence. It is shown that the Heisenberg spins of the same plaquette are twice stronger entangled in the two-fold degenerate quantum ground state than in the macroscopically degenerate quantum chiral one. The bipartite entanglement with chiral features completely disappears below or exactly at the critical temperature of the model, while that with no chirality may survive even above the critical temperature of the model. Non-monotonous temperature variations of the concurrence clearly evidence the activation of the entangled Heisenberg states also above classical ground state as well as their re-appearance above the critical temperature of the model.     

Monte Carlo study of the two dimensional quadratic ising ferromagnet with mixed spins ofS=1/2 andS=1

The single-spin-flip Metropolis algorithm is applied to an Ising ferromagnet with mixed spins ofS=1/2 andS=1 on the square lattice. The critical temperature obtained from our Monte Carlo simulation is very close to the high temperature series expansion result. The finite size scaling results for the exponents yield the two dimensional Ising values, which are in good agreement with those suggested by the universality hypothesis.     

Contribution of electron-nuclear interaction to the residual resistivity of metals

In nonmagnetic metals the spin-spin interaction of the electrons and nuclei makes a strongly magnetic field and temperature T dependent contribution to the residual resistivity. The nuclei act as magnetic impurities. For magnetic metals (Tb, Ho, Dy) with a high internal magnetic field, the nuclear contribution to the resistivity vanishes at low temperatures T, where the nuclear spins are ordered, and saturates at high temperatures T, where the nuclear spins are disordered—the analog of the Schottky effect for the nuclear specific heat. The electron-nuclear interaction can destroy superconductivity in metals with low critical magnetic fields under conditions of ferromagnetic ordering of the nuclear spins. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 3, 193–197 (10 August 1996)