1,931 research outputs found
New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
The Q matrix invented by Baxter in 1972 to solve the eight vertex model at
roots of unity exists for all values of N, the number of sites in the chain,
but only for a subset of roots of unity. We show in this paper that a new Q
matrix, which has recently been introduced and is non zero only for N even,
exists for all roots of unity. In addition we consider the relations between
all of the known Q matrices of the eight vertex model and conjecture functional
equations for them.Comment: 20 pages, 2 Postscript figure
COMPLETE SOLUTION OF THE XXZ-MODEL ON FINITE RINGS. DYNAMICAL STRUCTURE FACTORS AT ZERO TEMPERATURE.
The finite size effects of the dynamical structure factors in the XXZ-model
are studied in the euclidean time -representation. Away from the
critical momentum finite size effects turn out to be small except for
the large limit. The large finite size effects at the critical momentum
signal the emergence of infrared singularities in the spectral
-representation of the dynamical structure factors.Comment: PostScript file with 12 pages + 11 figures uuencoded compresse
The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity for odd N
Following Baxter's method of producing Q_{72}-operator, we construct the
Q-operator of the root-of-unity eight-vertex model for the crossing parameter
with odd where Q_{72} does not exist. We use this
new Q-operator to study the functional relations in the Fabricius-McCoy
comparison between the root-of-unity eight-vertex model and the superintegrable
N-state chiral Potts model. By the compatibility of the constructed Q-operator
with the structure of Baxter's eight-vertex (solid-on-solid) SOS model, we
verify the set of functional relations of the root-of-unity eight-vertex model
using the explicit form of the Q-operator and fusion weights of SOS model.Comment: Latex 28 page; Typos corrected, minor changes in presentation,
References added and updated-Journal versio
XXZ Bethe states as highest weight vectors of the loop algebra at roots of unity
We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at
roots of unity is a highest weight vector of the loop algebra, for some
restricted sectors with respect to eigenvalues of the total spin operator
, and evaluate explicitly the highest weight in terms of the Bethe roots.
We also discuss whether a given regular Bethe state in the sectors generates an
irreducible representation or not. In fact, we present such a regular Bethe
state in the inhomogeneous case that generates a reducible Weyl module. Here,
we call a solution of the Bethe ansatz equations which is given by a set of
distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero
Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio
Water quality of the Great Barrier Reef : distributions, effects on reef biota and trigger values for the protection of ecosystem health
This Report to the GBMPA provides technical background information and statistical
data analysis for defining improved water quality guideline trigger values for the GBR
Water Quality Guidelines
The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
We construct the explicit -operator incorporated with the
-loop-algebra symmetry of the six-vertex model at roots of unity. The
functional relations involving the -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 -state chiral
Potts model. We show that the whole set of functional equations is valid for
the -operator. Direct calculations in certain cases are also given here for
clearer illustration about the nature of the -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
Thermodynamical Properties of a Spin 1/2 Heisenberg Chain Coupled to Phonons
We performed a finite-temperature quantum Monte Carlo simulation of the
one-dimensional spin-1/2 Heisenberg model with nearest-neighbor interaction
coupled to Einstein phonons. Our method allows to treat easily up to 100
phonons per site and the results presented are practically free from truncation
errors. We studied in detail the magnetic susceptibility, the specific heat,
the phonon occupation, the dimerization, and the spin-correlation function for
various spin-phonon couplings and phonon frequencies. In particular we give
evidence for the transition from a gapless to a massive phase by studying the
finite-size behavior of the susceptibility. We also show that the dimerization
is proportional to for .Comment: 10 pages, 17 Postscript Figure
Single Top Quark Production and Decay at Next-to-leading Order in Hadron Collision
We present a calculation of the next-to-leading order QCD corrections, with
one-scale phase space slicing method, to single top quark production and decay
process at hadron colliders.
Using the helicity amplitude method, the angular correlation of the final state
partons and the spin correlation of the top quark are preserved. The effect of
the top quark width is also examined.Comment: 47 pages, 9 figure
Inherent structures dynamics in glasses: a comparative study
A comparative study of the dynamics of inherent structures at low
temperatures is performed on different models of glass formers: a three
dimensional Lennard-Jones binary mixture (LJBM), facilitated spin models
(either symmetrically constrained, SCIC, or asymmetrically, ACIC) and the trap
model. We use suitable correlation functions introduced in a previous work
which allow to distinguish the behaviour between models with or without spatial
or topological structure. Furthermore, the correlations between inherent
structures behave differently in the cases of strong (SCIC) and fragile (ACIC,
LJBM) glasses, as a consequence of the different role played by energy barriers
when the temperature is lowered. The similarities in the behaviour of the ACIC
and LJBM suggest a common nature of the glassy dynamics for both systems.Comment: Proceedings of NEXT2003 (News and Expectations in Thermostatistics,
Sardinia, Italy, september 2003
Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time Dynamics Study
The short-time dynamic evolution of an Ising model embedded in an infinitely
ramified fractal structure with noninteger Hausdorff dimension was studied
using Monte Carlo simulations. Completely ordered and disordered spin
configurations were used as initial states for the dynamic simulations. In both
cases, the evolution of the physical observables follows a power-law behavior.
Based on this fact, the complete set of critical exponents characteristic of a
second-order phase transition was evaluated. Also, the dynamic exponent of the critical initial increase in magnetization, as well as the critical
temperature, were computed. The exponent exhibits a weak dependence
on the initial (small) magnetization. On the other hand, the dynamic exponent
shows a systematic decrease when the segmentation step is increased, i.e.,
when the system size becomes larger. Our results suggest that the effective
noninteger dimension for the second-order phase transition is noticeably
smaller than the Hausdorff dimension. Even when the behavior of the
magnetization (in the case of the ordered initial state) and the
autocorrelation (in the case of the disordered initial state) with time are
very well fitted by power laws, the precision of our simulations allows us to
detect the presence of a soft oscillation of the same type in both magnitudes
that we attribute to the topological details of the generating cell at any
scale.Comment: 10 figures, 4 tables and 14 page
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