Decay of correlations in spin systems

We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation.     

Decay of correlations. IV. Necessary and sufficient conditions for a rapid decay of correlations

We considerN-particle systems whose probability distributions obey the master equation. For these systems, we derive the necessary and sufficient conditions under which the reducedn-particle (n) probabilities also obey master equations and under which the Ursell functions decay to their equilibrium values faster than the probability distributions. These conditions impose restrictions on the form of the transition rate matrix and thus on the form of its eigenfunctions. We first consider systems in which the eigenfunctions of theN-particle transition rate matrix are completely factorized and demonstrate that for such systems, the reduced probabilities obey master equations and the Ursell functions decay rapidly if certain additional conditions are imposed. As an example of such a system, we discuss a random walk ofN pairwise interacting walkers. We then demonstrate that for systems whoseN-particle transition matrix can be written as a sum of one-particle, two-particle, etc. contributions, and for which the reduced probabilities obey master equations, the reduced master equations become, in the thermodynamic limit, those for independent particles, which have been discussed by us previously. As an example of suchN-particle systems, we discuss the relaxation of a gas of interacting harmonic oscillators.Supported in part (grants to D.B. and K.E.S.) by the Advanced Research Projects Agency of the Department of Defense as monitored by the U.S. Office of Naval Research under Contract N00014-69-A-0200-6018, and in part (grant to I.O.) by the National Science Foundation.     

On the generalized Hermite-based lattice Boltzmann construction,lattice sets,weights, moments,distribution functions and high-order models

The influence of the use of the generalized Hermite polynomial on the Hermite-based lattice Bofiz- mann （LB） construction approach, lattice sets, the thermal weights, moments and the equilibrium distribution function （EDF） are addressed. A new moment system is proposed. The theoretical possibility to obtain a unique high-order Hermite-based singel relaxation time LB model capable to exactly inatch some first hydrodynamic inoments thermally i） on-Cartesian lattice, ii） with thermal weights in the EDF, iii） whilst the highest possible hydrodynamic moments that are exactly reatched are obtained with the shortest on-Cartesian lattiee sets with some fixed real-valued temperatures, is also analyzed.     

Explicit relations for the radial distribution functions for one-dimensional lattice (arbitrary spacing) fluids and solutions

It is pointed out that the size of the matrix required to formulate the grand partition function for a one-dimensional lattice fluid for a fixed and finite range of the interatomic potential varies linearly with the density of lattice points used and hence is much smaller and more manageable than the expected size (which varies exponentially with the same quantity) and thus allows very fine grids to be examined. Using the matrix treatment of the grand partition function, it is shown that the radial distribution function for a one-dimensional fluid or solution can be formulated as an explicit matrix product which is simply performed by computer. The resulting distribution functions (which can be extrapolated to the continuum by varying the lattice spacing) are useful as starting solutions for the iterative solution of integral equations for three-dimensional fluids.     

Response factorization of simply connected Ising lattices with application to bethe lattice spin glasses

The thermodynamics of a classical lattice gas in Ising form, with arbitrary interaction, is set up in entropy format, with multipoint magnetizations as control parameters. It is specialized to the case of one- and two-point interactions on a simply connected lattice; both entropy and profile equations are written down explicitly. Linear response functions are expressed in Wertheim-Baxter factorization and used to derive the Jacobian of the transformation from couplings to magnetizations. An arbitrary spin-glass coupling distribution is transformed to the corresponding magnetization distribution, whose effect on thermodynamic properties is assessed. A Gaussian coupling-fluctuation expansion diverges at sufficiently large fluctuation amplitude, suggesting the possibility of a phase transition.     

Long-range inverse two-spin correlations in one-dimensional Potts lattices

The inverse two-spin correlation function of a one-dimensional three-state Potts lattice with constant nearest-neighbor interactions in a uniform external field is derived exactly. It is shown that the external field induces long-range correlations. The inverse two-spin correlation function decays in a monotonie exponential fashion for a ferromagnetic lattice, while it decays in an oscillatory exponential fashion for an antiferromagnetic lattice. With no external field the inverse two-spin correlation function has a finite range equal to that of the interactions.     

Susceptibility and magnetisation of a random ising model

The susceptibility of a bond disordered Ising model is calculated by configurationally averaging an Ornstein-Zernike type of equation for the two spin correlation function. The equation for the correlation function is derived using a diagrammatic method due to Englert. The averaging is performed using bond CPA. The magnetisation is also calculated by averaging in a similar manner a linearised molecular field equation. Part of the work was done, while one of the authors (DK) was visiting International Centre for Theoretical Physics, Trieste, Italy.     

Loop effects in the Ising spin glass on the Bethe-like lattices

Equations for the spin glass order in the Ising spin glass model on the Bethe-like lattices with and without small loops are studied. For each lattice, equations are obtained by using and not using the replica method. Within the replica symmetric approximation, equations obtained by the two ways are shown to be identical. To see the effects of the small loops and the replica symmetry breaking, a spin glass order parameter is investigated as a function of the connectivity of the lattices close to the transition temperature. Replica symmetry breaking is enhanced by the existence of small loops.     

Decay of the remanent magnetization in the asymmetric spin chain

The dynamics of the one-dimensional spin glass with asymmetric interactions between neighboring spins is considered. We confine ourselves to discrete couplings with values ±J. We show that the algebraic decay of the remanent magnetization of the infinite ±J-spin chain at zero temperature is only valid for symmetric couplings. Our analytical investigations as well as computer simulations show stretched exponential decay for any finite concentration of antisymmetric bonds. Thus, the asymmetric ±J-spin chain shows an asymmetry-induced phase transition at zero temperature.     

纳米晶体线的晶格动力学格林函数及晶格振动

通过求解差分方程,推导了纳米晶体线的晶格动力学格林函数,分析了其晶格振动,并推导了声子数表象中的原子位移及晶格振动哈密顿公式.研究结果表明,纳米晶体线的晶格振动能带分裂为一系列的子带,格波只能沿纳米晶体线的纵向传播,沿纳米晶体线的横截面只存在驻波.     

Top quark spin correlations at the Tevatron and the LHC

Spin correlations of top quarks produced in hadron collisions have not been observed experimentally with large significance. In this Letter, we propose a new variable that may enable demonstration of the existence of spin correlations with 3–4 σ$3\text{–}4\sigma$ significance using just a few hundred dilepton events both at the Tevatron and the LHC. Such number of dilepton events has been observed at the Tevatron. At the LHC, it will become available once integrated luminosity of a few hundred inverse picobarns is collected.     

Correlation functions and boundary conditions in the ising ferromagnet

A number of new results on the Ising ferromagnet are obtained as a consequence of correlation inequalities. These results concern the monotonicity properties of the correlation functions, the study of equilibrium states for certain boundary conditions, and the uniqueness of the state in a semiinfinite lattice.     

Decay to equilibrium in random spin systems on a lattice. II

We study the continuous spin systems on ad3-dimensional lattice with random ferromagnetic interactions of finite range. We show that, if the temperature is sufficiently high and the probability of interaction to be large is small enough, the almost sure decay to equilibrium has a subexponential upper bound.     

Correlation functions of odd numbers of spins with finite separations on the Onsager-Ising lattice

A method is developed for making exact evaluations of correlation functions of odd numbers of spins on the Onsager-Ising lattice, applicable to cases in which the separations between the spins are finite. The method is based on an identity which permits the reduction of determinants of infinite-dimensional matrices to those of finite dimension. Particularly simple results are obtained when all spins are on a straight line. Numerical calculations are carried out for a few cases.     

Algebraic spatial correlations in lattice gas automata violating detailed balance

In this paper we discuss the existence of generic long-range correlations in spatially homogeneous and stable equilibrium states of closed lattice gas automata whose stochastic collision rules violate the symmetry conditions of detailed balance and in addition satisfy local conservation laws. Such correlations occur even though the collision rules are strictly local and invariant under all symmetries of the lattice. First a phenomenological (Langevin equation) approach is discussed. Next we present a theoretical analysis on the basis of an approximate microscopic (ring kinetic) theory. This theory is used to calculate the amplitude ofr ^– tails in the spatial correlations, and the result is compared with computer simulations.     

Critical point estimation and long-range behavior in the one-dimensional XY model using thermal quantum and total correlations

We investigate the thermal quantum and total correlations in the anisotropic XY spin chain in transverse field. While we adopt concurrence and geometric quantum discord to measure quantum correlations, we use measurement-induced non-locality and an alternative quantity defined in terms of Wigner–Yanase information to quantify total correlations. We show that the ability of these measures to estimate the critical point at finite temperature strongly depend on the anisotropy parameter of the Hamiltonian. We also identify a correlation measure which detects the factorized ground state in this model. Furthermore, we study the effect of temperature on long-range correlations.     

A mean-field,effective medium theory of random binary alloys III. The ising model with competing interactions

The Ising model with competing interactions is studied in a mean field effective medium approach. The phase diagram of such model alloys is studied. We conclude that for all ratios of the competing interaction moments, a spin glass phase always exists at low temperatures for certain concentration regimes.     

Decay of correlations in surface models

A convergent low-temperature expansion for a variety of models of twodimensional surfaces is presented. It yields existence of the thermodynamic limit for the pressure and correlation functions as well as analyticity inz =e ^– In addition, the estimates give exponential decay of truncated correlations, which proves the existence of a gap in the spectrum of the transfer matrix below the ground state eigenvalue. Two particular examples included in the general framework are the solid-on-solid and discrete Gaussian models.Supported in part by the National Science Foundation under grant No. PHY 79-16812.     

Uniqueness and exponential decay of correlations for some two-dimensional spin lattice systems

We consider a two-dimensional lattice spin system which naturally arises in dynamical systems called coupled map lattice. The configuration space of the spin system is a direct product of mixing subshifts of finite type. The potential is defined on the set of all squares in Z² and decays exponentially with the linear size of the square. Via the polymer expansion technique we prove that for sufficiently high temperatures the limit Gibbs distribution is unique and has an exponential decay of correlations.     

Ground-state and quenched-state properties of a one-dimensional interacting lattice gas in a random potential

We determine the zero-temperature properties of a one-dimensional lattice gas of particles that interact via a nearest neighbor exclusion potential and are subject to a random external field. The model is a special limiting case of the random field Ising chain. We calculate (1) the energy and density of the ground state as well as the local energy-density correlation and (2) the pair correlation function. The latter calculation gives access to all higher order correlations. The structure factor is shown to be a squared Lorentzian. We also compare the ground state to the quenched state obtained by sequentially filling the lowest available energy levels.