Evidence for a first order transition in a plaquette 3d Ising-like action

We investigate a 3d Ising action which corresponds to a a class of models defined by Savvidy and Wegner, originally intended as discrete versions of string theories on cubic lattices. These models have vanishing bare surface tension and the couplings are tuned in such a way that the action depends only on the angles of the discrete surface, i.e. on the way the surface is embedded in ${\bf Z}^3$. Hence the name gonihedric by which they are known. We show that the model displays a rather clear first order phase transition in the limit where self-avoidance is neglected and the action becomes a plaquette one. This transition persists for small values of the self avoidance coupling, but it turns to second order when this latter parameter is further increased. These results exclude the use of this type of action as models of gonihedric random surfaces, at least in the limit where self avoidance is neglected.Comment: 4 pages Latex text, 4 postscript figure

Theory of Low Temperature Electron Spin Resonance in Half-integer Spin Antiferromagnetic Chains

A theory of low temperature (T) electron spin resonance (ESR) in half-integer spin antiferromagnetic chains is developed using field theory methods and avoiding previous approximations. It is compared to experiments on Cu benzoate. Power laws are predicted for the line-width broadening due to various types of anisotropy. At T -> 0, zero width absorption peaks occur in some cases. The second ESR peak in Cu benzoate, observed at T<.76K, is argued not to indicate Neel order as previously claimed, but to correspond to a sine-Gordon "breather" excitation.Comment: 4 pages, REVTEX, 3 PostScript figures embedded in tex

Glassy transition and metastability in four-spin Ising model

Using Monte Carlo simulations we show that the three-dimensional Ising model with four-spin (plaquette) interactions has some characteristic glassy features. The model dynamically generates diverging energy barriers, which give rise to slow dynamics at low temperature. Moreover, in a certain temperature range the model possesses a metastable (supercooled liquid) phase, which is presumably supported by certain entropy barriers. Although extremely strong, metastability in our model is only a finite-size effect and sufficiently large droplets of stable phase divert evolution of the system toward the stable phase. Thus, the glassy transitions in this model is a dynamic transition, preceded by a pronounced peak in the specific heat.Comment: extensively revised, with further simulations of metastability properties, response to referees tactfully remove

Difference Equations and Highest Weight Modules of U_q[sl(n)]

The quantized version of a discrete Knizhnik-Zamolodchikov system is solved by an extension of the generalized Bethe Ansatz. The solutions are constructed to be of highest weight which means they fully reflect the internal quantum group symmetry.Comment: 9 pages, LaTeX, no figure

String tension in gonihedric 3D Ising models

For the 3D gonihedric Ising models defined by Savvidy and Wegner the bare string tension is zero and the energy of a spin interface depends only on the number of bends and self-intersections, in antithesis to the standard nearest-neighbour 3D Ising action. When the parameter kappa weighting the self-intersections is small the model has a first order transition and when it is larger the transition is continuous. In this paper we investigate the scaling of the renormalized string tension, which is entirely generated by fluctuations, using Monte Carlo simulations This allows us to obtain an estimate for the critical exponents alpha and nu using both finite-size-scaling and data collapse for the scaling function.Comment: Latex + postscript figures. 8 pages text plus 7 figures, spurious extra figure now removed

The Q-operator for Root-of-Unity Symmetry in Six Vertex Model

We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-operator, the six-vertex transfer matrix and fusion matrices are derived from the Bethe equation, parallel to the Onsager-algebra-symmetry discussion in the superintegrable $N$-state chiral Potts model. We show that the whole set of functional equations is valid for the $Q$-operator. Direct calculations in certain cases are also given here for clearer illustration about the nature of the $Q$-operator in the symmetry study of root-of-unity six-vertex model from the functional-relation aspect.Comment: Latex 26 Pages; Typos and small errors corrected, Some explanations added for clearer presentation, References updated-Journal version with modified labelling of sections and formula

Quantum Group Invariant Supersymmetric t-J Model with periodic boundary conditions

An integrable version of the supersymmetric t-J model which is quantum group invariant as well as periodic is introduced and analysed in detail. The model is solved through the algebraic nested Bethe ansatz method.Comment: 11 pages, LaTe

Bethe ansatz solution of the closed anisotropic supersymmetric U model with quantum supersymmetry

The nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for the energy is given.Comment: 7 pages (revtex), minor modifications. To appear in Mod. Phys. Lett.

Yang-Baxter equation and reflection equations in integrable models

The definitions of the main notions related to the quantum inverse scattering methods are given. The Yang-Baxter equation and reflection equations are derived as consistency conditions for the factorizable scattering on the whole line and on the half-line using the Zamolodchikov-Faddeev algebra. Due to the vertex-IRF model correspondence the face model analogue of the ZF-algebra and the IRF reflection equation are written down as well as the $Z_2$-graded and colored algebra forms of the YBE and RE.Comment: 21 pages, Latex, Lectures in Schladming school of theoretical physics (March 1995

Constructing Infinite Particle Spectra

We propose a general construction principle which allows to include an infinite number of resonance states into a scattering matrix of hyperbolic type. As a concrete realization of this mechanism we provide new S-matrices generalizing a class of hyperbolic ones, which are related to a pair of simple Lie algebras, to the elliptic case. For specific choices of the algebras we propose elliptic generalizations of affine Toda field theories and the homogeneous sine-Gordon models. For the generalization of the sinh-Gordon model we compute explicitly renormalization group scaling functions by means of the c-theorem and the thermodynamic Bethe ansatz. In particular we identify the Virasoro central charges of the corresponding ultraviolet conformal field theories.Comment: 7 pages Latex, 7 figures (typo in figure 3 corrected