8,240 research outputs found
Ex-nihilo: Obstacles Surrounding Teaching the Standard Model
The model of the Big Bang is an integral part of the national curriculum for
England. Previous work (e.g. Baxter 1989) has shown that pupils often come into
education with many and varied prior misconceptions emanating from both
internal and external sources. Whilst virtually all of these misconceptions can
be remedied, there will remain (by its very nature) the obstacle of ex-nihilo,
as characterised by the question `how do you get something from nothing?' There
are two origins of this obstacle: conceptual (i.e. knowledge-based) and
cultural (e.g. deeply held religious viewpoints). The article shows how the
citizenship section of the national curriculum, coming `online' in England from
September 2002, presents a new opportunity for exploiting these.Comment: 6 pages. Accepted for publication in Physics E
General scalar products in the arbitrary six-vertex model
In this work we use the algebraic Bethe ansatz to derive the general scalar
product in the six-vertex model for generic Boltzmann weights. We performed
this calculation using only the unitarity property, the Yang-Baxter algebra and
the Yang-Baxter equation. We have derived a recurrence relation for the scalar
product. The solution of this relation was written in terms of the domain wall
partition functions. By its turn, these partition functions were also obtained
for generic Boltzmann weights, which provided us with an explicit expression
for the general scalar product.Comment: 24 page
Analyticity and Integrabiity in the Chiral Potts Model
We study the perturbation theory for the general non-integrable chiral Potts
model depending on two chiral angles and a strength parameter and show how the
analyticity of the ground state energy and correlation functions dramatically
increases when the angles and the strength parameter satisfy the integrability
condition. We further specialize to the superintegrable case and verify that a
sum rule is obeyed.Comment: 31 pages in harvmac including 9 tables, several misprints eliminate
Analytic solutions of the 1D finite coupling delta function Bose gas
An intensive study for both the weak coupling and strong coupling limits of
the ground state properties of this classic system is presented. Detailed
results for specific values of finite are given and from them results for
general are determined. We focus on the density matrix and concomitantly
its Fourier transform, the occupation numbers, along with the pair correlation
function and concomitantly its Fourier transform, the structure factor. These
are the signature quantities of the Bose gas. One specific result is that for
weak coupling a rational polynomial structure holds despite the transcendental
nature of the Bethe equations. All these new results are predicated on the
Bethe ansatz and are built upon the seminal works of the past.Comment: 23 pages, 0 figures, uses rotate.sty. A few lines added. Accepted by
Phys. Rev.
Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions
We consider the six-vertex model with anti-periodic boundary conditions
across a finite strip. The row-to-row transfer matrix is diagonalised by the
`commuting transfer matrices' method. {}From the exact solution we obtain an
independent derivation of the interfacial tension of the six-vertex model in
the anti-ferroelectric phase. The nature of the corresponding integrable
boundary condition on the spin chain is also discussed.Comment: 18 pages, LaTeX with 1 PostScript figur
Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
We connect two alternative concepts of solving integrable models, Baxter's
method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz.
The main steps of the calculation are performed in a general setting and a
formula for the Bethe eigenvalues of the Q-operator is derived. A proof is
given for states which contain up to three Bethe roots. Further evidence is
provided by relating the findings to the six-vertex fusion hierarchy. For the
XXZ spin-chain we analyze the cases when the deformation parameter of the
underlying quantum group is evaluated both at and away from a root of unity.Comment: 32 page
Bethe Equations "on the Wrong Side of Equator"
We analyse the famous Baxter's equations for () spin chain
and show that apart from its usual polynomial (trigonometric) solution, which
provides the solution of Bethe-Ansatz equations, there exists also the second
solution which should corresponds to Bethe-Ansatz beyond . This second
solution of Baxter's equation plays essential role and together with the first
one gives rise to all fusion relations.Comment: 13 pages, original paper was spoiled during transmissio
Ferrimagnetism of dilute Ising antiferromagnets
It is shown that nearest-neighbor antiferromagnetic interactions of identical
Ising spins on imbalanced bipartite lattice and imbalanced bipartite
hierarchical fractal result in ferrimagnetic order instead of antiferromagnetic
one. On some crystal lattices dilute Ising antiferromagnets may also become
ferrimagnets due to the imbalanced nature of the magnetic percolation cluster
when it coexists with the percolation cluster of vacancies. As evidenced by the
existing experiments on , such ferrimagnetism is inherent
property of bcc lattice so thermodynamics of these compounds at low can be
similar to that of antiferromagnet on imbalanced hierarchical fractal.Comment: 6 pages, 4 figure
A Potts/Ising Correspondence on Thin Graphs
We note that it is possible to construct a bond vertex model that displays
q-state Potts criticality on an ensemble of phi3 random graphs of arbitrary
topology, which we denote as ``thin'' random graphs in contrast to the fat
graphs of the planar diagram expansion.
Since the four vertex model in question also serves to describe the critical
behaviour of the Ising model in field, the formulation reveals an isomorphism
between the Potts and Ising models on thin random graphs. On planar graphs a
similar correspondence is present only for q=1, the value associated with
percolation.Comment: 6 pages, 5 figure
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