10,666 research outputs found
A direct proof of Kim's identities
As a by-product of a finite-size Bethe Ansatz calculation in statistical
mechanics, Doochul Kim has established, by an indirect route, three
mathematical identities rather similar to the conjugate modulus relations
satisfied by the elliptic theta constants. However, they contain factors like
and , instead of . We show here that
there is a fourth relation that naturally completes the set, in much the same
way that there are four relations for the four elliptic theta functions. We
derive all of them directly by proving and using a specialization of
Weierstrass' factorization theorem in complex variable theory.Comment: Latex, 6 pages, accepted by J. Physics
Entropy of Folding of the Triangular Lattice
The problem of counting the different ways of folding the planar triangular
lattice is shown to be equivalent to that of counting the possible 3-colorings
of its bonds, a dual version of the 3-coloring problem of the hexagonal lattice
solved by Baxter. The folding entropy Log q per triangle is thus given by
Baxter's formula q=sqrt(3)(Gamma[1/3])^(3/2)/2pi =1.2087...Comment: 9 pages, harvmac, epsf, uuencoded, 5 figures included, Saclay
preprint T/9401
High temperature materials study
High temperature operating electronic devices for vapor deposition reactor syste
Bethe Ansatz Equations for the Broken -Symmetric Model
We obtain the Bethe Ansatz equations for the broken -symmetric
model by constructing a functional relation of the transfer matrix of
-operators. This model is an elliptic off-critical extension of the
Fateev-Zamolodchikov model. We calculate the free energy of this model on the
basis of the string hypothesis.Comment: 43 pages, latex, 11 figure
High-temperature-materials study
Chemical vapor deposition of aluminum phosphides onto single crystals of silicon and gallium arsenide for producing high temperature operating solid state electronic device
Critical and Tricritical Hard Objects on Bicolorable Random Lattices: Exact Solutions
We address the general problem of hard objects on random lattices, and
emphasize the crucial role played by the colorability of the lattices to ensure
the existence of a crystallization transition. We first solve explicitly the
naive (colorless) random-lattice version of the hard-square model and find that
the only matter critical point is the non-unitary Lee-Yang edge singularity. We
then show how to restore the crystallization transition of the hard-square
model by considering the same model on bicolored random lattices. Solving this
model exactly, we show moreover that the crystallization transition point lies
in the universality class of the Ising model coupled to 2D quantum gravity. We
finally extend our analysis to a new two-particle exclusion model, whose
regular lattice version involves hard squares of two different sizes. The exact
solution of this model on bicolorable random lattices displays a phase diagram
with two (continuous and discontinuous) crystallization transition lines
meeting at a higher order critical point, in the universality class of the
tricritical Ising model coupled to 2D quantum gravity.Comment: 48 pages, 13 figures, tex, harvmac, eps
Ground State of the Quantum Symmetric Finite Size XXZ Spin Chain with Anisotropy Parameter
We find an analytic solution of the Bethe Ansatz equations (BAE) for the
special case of a finite XXZ spin chain with free boundary conditions and with
a complex surface field which provides for symmetry of the
Hamiltonian. More precisely, we find one nontrivial solution, corresponding to
the ground state of the system with anisotropy parameter
corresponding to .Comment: 6 page
Directed-loop Monte Carlo simulations of vertex models
We show how the directed-loop Monte Carlo algorithm can be applied to study
vertex models. The algorithm is employed to calculate the arrow polarization in
the six-vertex model with the domain wall boundary conditions (DWBC). The model
exhibits spatially separated ordered and ``disordered'' regions. We show how
the boundary between these regions depends on parameters of the model. We give
some predictions on the behavior of the polarization in the thermodynamic limit
and discuss the relation to the Arctic Circle theorem.Comment: Extended version with autocorrelations and more figures. Added 2
reference
Interpenetration as a Mechanism for Liquid-Liquid Phase Transitions
We study simple lattice systems to demonstrate the influence of
interpenetrating bond networks on phase behavior. We promote interpenetration
by using a Hamiltonian with a weakly repulsive interaction with nearest
neighbors and an attractive interaction with second-nearest neighbors. In this
way, bond networks will form between second-nearest neighbors, allowing for two
(locally) distinct networks to form. We obtain the phase behavior from analytic
solution in the mean-field approximation and exact solution on the Bethe
lattice. We compare these results with exact numerical results for the phase
behavior from grand canonical Monte Carlo simulations on square, cubic, and
tetrahedral lattices. All results show that these simple systems exhibit rich
phase diagrams with two fluid-fluid critical points and three thermodynamically
distinct phases. We also consider including third-nearest-neighbor
interactions, which give rise to a phase diagram with four critical points and
five thermodynamically distinct phases. Thus the interpenetration mechanism
provides a simple route to generate multiple liquid phases in single-component
systems, such as hypothesized in water and observed in several model and
experimental systems. Additionally, interpenetration of many such networks
appears plausible in a recently considered material made from nanoparticles
functionalized by single strands of DNA.Comment: 12 pages, 9 figures, submitted to Phys. Rev.
Star-Triangle Relation for a Three Dimensional Model
The solvable -chiral Potts model can be interpreted as a
three-dimensional lattice model with local interactions. To within a minor
modification of the boundary conditions it is an Ising type model on the body
centered cubic lattice with two- and three-spin interactions. The corresponding
local Boltzmann weights obey a number of simple relations, including a
restricted star-triangle relation, which is a modified version of the
well-known star-triangle relation appearing in two-dimensional models. We show
that these relations lead to remarkable symmetry properties of the Boltzmann
weight function of an elementary cube of the lattice, related to spatial
symmetry group of the cubic lattice. These symmetry properties allow one to
prove the commutativity of the row-to-row transfer matrices, bypassing the
tetrahedron relation. The partition function per site for the infinite lattice
is calculated exactly.Comment: 20 pages, plain TeX, 3 figures, SMS-079-92/MRR-020-92. (corrupted
figures replaced
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