Two-Column Higher-Spin Massless Fields in AdS d Space

We consider a particular class of AdS _d mixed-symmetry bosonic massless fields corresponding to arbitrary two-column Young tableaux. We find unique gauge-invariant free actions and analyze the equations of motion.     

Universal Long-Time Relaxation on Lattices of Classical Spins: Markovian Behavior on Non-Markovian Timescales

The long-time behavior of certain fast-decaying infinite temperature correlation functions on one-, two-, and three-dimensional lattices of classical spins with various kinds of nearest-neighbor interactions is studied numerically, and evidence is presented that the functional form of this behavior is either simple exponential or exponential multiplied by cosine. Due to the fast characteristic timescale of the long-time decay, such a universality cannot be explained on the basis of conventional Markovian assumptions. It is suggested that this behavior is related to the chaotic properties of the spin dynamics.     

Convergence of block spins defined by a random field

We study the asymptotic behavior of families of dependent random variables called block spins, which are associated with random fields arising in statistical mechanics. We give sufficient conditions for these families to converge weakly to products of independent Gaussian random variables. We also estimate the error terms involved. In addition we give some conditions which imply that the block spins can converge weakly only to families of normal or degenerate random variables. Central to our proofs is a mixing property which is weaker than strong mixing and which holds for many random fields studied in statistical mechanics. Finally we give a simple method for determining when a stationary random field does not satisfy a strong mixing property. This method implies that the two-dimensional Ising model at the critical temperature is not strong mixing, a result obtained by a different method by M. Cassandro and G. Jona-Lasinio. The method also shows that a stationary, mean-zero, positively correlated Gaussian process indexed by is not strong mixing if its covariance function decreases liket ^– , 0 < < 1.     

Improved Monte Carlo renormalization group method

An extensive program to analyze critical systems using an improved Monte Carlo renormalization group method (IMCRG),⁽¹⁾ being undertaken at LANL and Cornell, is described. Here we first briefly rview the method and then list some of the topics being investigated.     

Berry phase of coupled two arbitrary spins in a time-varying magnetic field

In this paper, we investigate the Berry phase of two coupled arbitrary spins driven by a time-varying magnetic field where the Hamiltonian is explicitly time-dependent. Using a technique of time-dependent gauge transform the Berry phase and time-evolution operator are found explicitly in the adiabatic approximation. The general solutions for arbitrary spins are applied to the spin-1/2\ system as an example of explanation.     

The equivalence between B—W and K—G and R—S equations

The equivalence between the Bargmann--Wigner (B-W) equations and the Klein--Gordon (K-G) equations for integral spin, and the Rarita--Schwinger (R-S) equations for half integral spin is established by explicit derivation, starting from the lowest spin cases. It is demonstrated that all the constraints or subsidiary conditions imposed on the K-G or R-S equations are included in the B-W equations.     

Curie and Pauli Spins in Lithium Intercalated MCMB

The lithium-intercalated carbon was originally a laboratory treasure of physicists, but it has now become the key material for the rechargeable lithium battery, which has the highest specific energy among all known chemical power sources. Although numerous techniques have been invoked to study the structure-property relationship of lithium-intercalated carbons, the problem has not been fully solved so far. There are only a few papers reporting ESR (electron spin resonance) studies of lithium …     

Expansions for One Quasiparticle States in Spin 1/2 Systems

Convergent expansions of the wavefunctions for the ground state and lowlying excited states of quantum transverse Ising systems are obtained. These expansions are employed to prove that the dispersion relation for a single quasi-particle has a convergent expansion.     

Phase diagram and critical properties of the asymmetric Mattis model

We extend the well-known Mattis model to the case of asymmetric bond distributions. Although the partition function is identical with that of the pure ferromagnetic Ising model (FIM) when the external field is absent, the response to the external field is nontrivial even at zero field. There are some exact relations between the present model and the FIM in the correlation functions, from which the phase diagram and critical exponents can be determined. Multicritical behavior and some other interesting phenomena typical for a random system are demonstrated by this model.     

Grain- and macro-scale kinematics for granular micromechanics based small deformation micromorphic continuum model

Macro-scale deformation of granular solids comprising large number of grains (>10⁶) are most efficiently described within the framework of continuum mechanics. It is notable, however that the micro-scale deformations in these materials are concentrated at the grain-boundaries or grain-contacts. Thus, the deformation energies in these systems must be modeled by considering the deformations concentrated in the neighborhood of the grain-boundaries or grain-contacts. To address this issue, grain-interactions has been widely described in the Hertzian sense by considering the relative movement of points on either side of a grain boundary or contact treated as an imperfect interface. This communication introduces the relevant kinematic variables given in the terms of the grain displacements, spins and size that can be used to estimate the relative movement of a grain boundary or contact. The macro-scale kinematic variables useful for continuum modeling are then identified with the grain-scale kinematic variables. The deformation energy density of the granular solid can thus be expressed both in terms of the grain-scale as well as the macro-scale kinematic variables providing the necessary pathway for micro-macro identification which can lead to non-classical micromorphic continuum models that incorporate grain-scale representation.