Semiclassical description of spin ladders

The Heisenberg spin ladder is studied in the semiclassical limit, via a mapping to the nonlinear $\sigma$ model. Different treatments are needed if the inter-chain coupling $K$ is small, intermediate or large. For intermediate coupling a single nonlinear $\sigma$ model is used for the ladder. Its predicts a spin gap for all nonzero values of $K$ if the sum $s+\tilde s$ of the spins of the two chains is an integer, and no gap otherwise. For small $K$, a better treatment proceeds by coupling two nonlinear sigma models, one for each chain. For integer $s=\tilde s$, the saddle-point approximation predicts a sharp drop in the gap as $K$ increases from zero. A Monte-Carlo simulation of a spin 1 ladder is presented which supports the analytical results.Comment: 8 pages, RevTeX 3.0, 4 PostScript figure

Quantum Heisenberg Chain with Long-Range Ferromagnetic Interactions at Low Temperature

A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. Low-temperature properties of this model are investigated. The susceptibility and the specific heat are calculated; the relation between their behaviors and strength of the long-range interactions is obtained. This model includes both the Haldane-Shastry model and the nearest-neighbor Heisenberg model; the corresponding results in this paper are in agreement with the solutions of both the models. It is shown that there exists an ordering transition in the region where the model has longer-range interactions than the HS model. The critical temperature is estimated.Comment: 17 pages(LaTeX REVTeX), 1 figure appended (PostScript), Technical Report of ISSP A-274

Quantum Spin Chains and Riemann Zeta Function with Odd Arguments

Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in thermodynamics limit. We prove that for short strings the probability can be expressed in terms of Riemann zeta function with odd arguments.Comment: LaTeX, 7 page

Entropy production by Q-ball decay for diluting long-lived charged particles

The cosmic abundance of a long-lived charged particle such as a stau is tightly constrained by the catalyzed big bang nucleosynthesis. One of the ways to evade the constraints is to dilute those particles by a huge entropy production. We evaluate the dilution factor in a case that non-relativistic matter dominates the energy density of the universe and decays with large entropy production. We find that large Q balls can do the job, which is naturally produced in the gauge-mediated supersymmetry breaking scenario.Comment: 8 pages, 1 figur

Exact results for the 1D interacting mixed Bose-Fermi gas

The exact solution of the 1D interacting mixed Bose-Fermi gas is used to calculate ground-state properties both for finite systems and in the thermodynamic limit. The quasimomentum distribution, ground-state energy and generalized velocities are obtained as functions of the interaction strength both for polarized and non-polarized fermions. We do not observe any demixing instability of the system for repulsive interactions.Comment: 12 pages, 4 figures, better comparison with hydrodynamic approach, typos corrected, references added, improved figure

The Evolution of Globular Clusters in the Galaxy

We investigate the evolution of globular clusters using N-body calculations and anisotropic Fokker-Planck (FP) calculations. The models include a mass spectrum, mass loss due to stellar evolution, and the tidal field of the parent galaxy. Recent N-body calculations have revealed a serious discrepancy between the results of N-body calculations and isotropic FP calculations. The main reason for the discrepancy is an oversimplified treatment of the tidal field employed in the isotropic FP models. In this paper we perform a series of calculations with anisotropic FP models with a better treatment of the tidal boundary and compare these with N-body calculations. The new tidal boundary condition in our FP model includes one free parameter. We find that a single value of this parameter gives satisfactory agreement between the N-body and FP models over a wide range of initial conditions. Using the improved FP model, we carry out an extensive survey of the evolution of globular clusters over a wide range of initial conditions varying the slope of the mass function, the central concentration, and the relaxation time. The evolution of clusters is followed up to the moment of core collapse or the disruption of the clusters in the tidal field of the parent galaxy. In general, our model clusters, calculated with the anisotropic FP model with the improved treatment for the tidal boundary, live longer than isotropic models. The difference in the lifetime between the isotropic and anisotropic models is particularly large when the effect of mass loss via stellar evolution is rather significant. On the other hand the difference is small for relaxation- dominated clusters which initially have steep mass functions and high central concentrations.Comment: 36 pages, 11 figures, LaTeX; added figures and tables; accepted by Ap

Fundamental Cycle of a Periodic Box-Ball System

We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.Comment: 28 pages, 6 figure

Spin-Wave Theory of the Spiral Phase of the t-J Model

A graded H.P,realization of the SU(2|1) algebra is proposed.A spin-wave theory with a condition that the sublattice magnetization is zero is discussed.The long-range spiral phase is investigated.The spin-spin correlator is calculated.Comment: 17 page

Excitation Spectrum of S=1S=1 Antiferromagnetic Chains

The dynamical structure factor $S(Q,\omega)$ of the $S=1$ antiferromagnetic Heisenberg chain with length 20 at zero temperature is calculated. The lowest energy states have the delta-function peak at the region $\pi\ge \vert Q\vert >0.3\pi$. At $\vert Q\vert<0.3\pi$ the lowest energy states are the lower-edge of the continuum of the scattering state, the strength of which decreases for large systems. This gives a reasonable explanation for the experimental fact that no clear peak is observed at the region $Q<0.3\pi$. This situation is more apparent for valence-bond solid state. On the contrary for $S=1/2$ antiferromagnetic Heisenberg chain the lowest energy states are always the edge of the continuum.Comment: 14pages, Revtex 3.0, No.279