Critical behaviour of a spin-tube model in a magnetic field

We show that the low-energy physics of the spin-tube model in presence of a critical magnetic field can be described by a broken SU(3) spin chain. Using the Lieb-Schultz-Mattis Theorem we characterize the possible magnetization plateaus and study the critical behavior in the region of transition between the plateaus m=1/2 and m=3/2 by means of renormalization group calculations performed on the bosonized effective continuum field theory. We show that in certain regions of the parameter space of the effective theory the system remains gapless, and we compute the spin-spin correlation functions in these regions. We also discuss the possibility of a plateau at m=1, and show that although there exists in the continuum theory a term that might cause the appearance of a plateau there, such term is unlikely to be relevant. This conjecture is proved by DMRG techniques. The modifications of the three-leg ladder Hamiltonian that might show plateaus at m =1,5/6,7/6 are discussed, and we give the expected form of correlation functions on the m=1 plateau.Comment: RevTeX, 43 pages, 5 EPS figure

Phase diagram of a 1 dimensional spin-orbital model

We study a 1 dimensional spin-orbital model using both analytical and numerical methods. Renormalization group calculations are performed in the vicinity of a special integrable point in the phase diagram with SU(4) symmetry. These indicate the existence of a gapless phase in an extended region of the phase diagram, missed in previous studies. This phase is SU(4) invariant at low energies apart from the presence of different velocities for spin and orbital degrees of freedom. The phase transition into a gapped dimerized phase is in a generalized Kosterlitz-Thouless universality class. The phase diagram of this model is sketched using the density matrix renormalization group technique.Comment: 11 pages, 5 figures, new references adde

Stability of fixed points in the (4+\epsilon)-dimensional random field O(N) spin model for sufficiently large N

We study the stability of fixed points in the two-loop renormalization group for the random field O($N$) spin model in $4+\epsilon$ dimensions. We solve the fixed-point equation in the 1/N expansion and $\epsilon$ expansion. In the large-N limit, we study the stability of all fixed points. We solve the eigenvalue equation for the infinitesimal deviation from the fixed points under physical conditions on the random anisotropy function. We find that the fixed point corresponding to dimensional reduction is singly unstable and others are unstable or unphysical. Therefore, one has no choice other than dimensional reduction in the large-N limit. The two-loop $\beta$ function enables us to find a compact area in the $(d, N)$ plane where the dimensional reduction breaks down. We calculate higher-order corrections in the 1/N and $\epsilon$ expansions to the fixed point. Solving the corrected eigenvalue equation nonperturbatively, we find that this fixed point is singly unstable also for sufficiently large $N$ and the critical exponents show a dimensional reduction.Comment: 9 pages, 2 figure

On gonihedric loops and quantum gravity

We present an analysis of the gonihedric loop model, a reformulation of the two dimensional gonihedric spin model, using two different techniques. First, the usual regular lattice statistical physics problem is mapped onto a height model and studied analytically. Second, the gravitational version of this loop model is studied via matrix models techniques. Both methods lead to the conclusion that the model has $c_{matter}=0$ for all values of the parameters of the model. In this way it is possible to understand the absence of a continuous transition

Antiferromagnetic S=1/2 Heisenberg Chain and the Two-flavor Massless Schwinger Model

An antiferromagnetic S=1/2 Heisenberg chain is mapped to the two-flavor massless Schwinger model at \theta=\pi. The electromagnetic coupling constant and velocity of light in the Schwinger model are determined in terms of the Heisenberg coupling and lattice spacing in the spin chain system.Comment: 3 pages. LaTex2

Smooth Paths on Three Dimensional Lattice

A particular class of random walks with a spin factor on a three dimensional cubic lattice is studied. This three dimensional random walk model is a simple generalization of random walk for the two dimensional Ising model. All critical diffusion constants and associated critical exponents are calculated. Continuum field theories such as Klein-Gordon, Dirac and massive Chern-Simons theories are constructed near several critical points.Comment: 7 pages,NUP-A-94-

Effect of Hund coupling in the one-dimensional SU(4) Hubbard model

The one-dimensional SU(4) Hubbard model perturbed by Hund coupling is studied, away from half-filling, by means of renormalization group and bosonization methods. A spectral gap is always present in the spin-orbital sector irrespective of the magnitude of the Coulomb repulsion. We further distinguish between two qualitatively different regimes. At small Hund coupling, we find that the symmetry of the system is dynamically enlarged to SU(4) at low energy with the result of {\it coherent} spin-orbital excitations. When the charge sector is not gapped, a superconducting instability is shown to exist. At large Hund coupling, the symmetry is no longer enlarged to SU(4) and the excitations in the spin sector become {\it incoherent}. Furthermore, the superconductivity can be suppressed in favor of the conventional charge density wave state.Comment: 10 pages, 1 figur

Geochemical Assessment of Vulnerability of Groundwater to Contaminant at Phuoc Hiep Landfill Site, Ho Chi Minh City, Vietnam

Abstract A geochemical assessment on vulnerability of groundwater quality and shallow aquifer in the vicinity of the Phuoc Hiep landfill site was carried out with a hydro-chemical approach for identifying various geochemical processes and understanding the impacts of landfill leachate on groundwater quality. Results indicate that hardness, nitrate, fluoride, iron in groundwater and heavy metal in surface water are above the standard for drinking water. Leachate seepage from the landfill is a main contaminant source of groundwater of Na-Cl water type with electrical conductivity (EC) values of 4,275 to 4,575 μS/cm. The pH values of the leachate are between 5.8 and 6.6. Concentrations of Al, Fe and Mn and heavy metals (Pb, Zn and Cu) in the leachate are above the drinking water standards. As a result, the waste leachate has a high content of contaminant that affects groundwater quality in highly productive zones. Two main zones of the aquifer were determined to be most vulnerable using GOD vulnerability model. Thus, these vulnerable zones are not suitable for waste disposal and the aquifer should be protected from leachate