748 research outputs found
Critical behaviour of the two-dimensional Ising susceptibility
We report computations of the short-distance and the long-distance (scaling)
contributions to the square-lattice Ising susceptibility in zero field close to
T_c. Both computations rely on the use of nonlinear partial difference
equations for the correlation functions. By summing the correlation functions,
we give an algorithm of complexity O(N^6) for the determination of the first N
series coefficients. Consequently, we have generated and analysed series of
length several hundred terms, generated in about 100 hours on an obsolete
workstation. In terms of a temperature variable, \tau, linear in T/T_c-1, the
short-distance terms are shown to have the form \tau^p(ln|\tau|)^q with p>=q^2.
To O(\tau^14) the long-distance part divided by the leading \tau^{-7/4}
singularity contains only integer powers of \tau. The presence of irrelevant
variables in the scaling function is clearly evident, with contributions of
distinct character at leading orders |\tau|^{9/4} and |\tau|^{17/4} being
identified.Comment: 11 pages, REVTex
Identities in the Superintegrable Chiral Potts Model
We present proofs for a number of identities that are needed to study the
superintegrable chiral Potts model in the sector.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 11 pages,
uses eufb10 and eurm10 fonts. Typeset twice! vs2: Two equations added. vs3:
Introduction adde
Overlapping Unit Cells in 3d Quasicrystal Structure
A 3-dimensional quasiperiodic lattice, with overlapping unit cells and
periodic in one direction, is constructed using grid and projection methods
pioneered by de Bruijn. Each unit cell consists of 26 points, of which 22 are
the vertices of a convex polytope P, and 4 are interior points also shared with
other neighboring unit cells. Using Kronecker's theorem the frequencies of all
possible types of overlapping are found.Comment: LaTeX2e, 11 pages, 5 figures (8 eps files), uses iopart.class. Final
versio
New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
In this paper we show how an infinite system of coupled Toda-type nonlinear
differential equations derived by one of us can be used efficiently to
calculate the time-dependent pair-correlations in the Ising chain in a
transverse field. The results are seen to match extremely well long large-time
asymptotic expansions newly derived here. For our initial conditions we use new
long asymptotic expansions for the equal-time pair correlation functions of the
transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising
model. Using this one can also study the equal-time wavevector-dependent
correlation function of the quantum chain, a.k.a. the q-dependent diagonal
susceptibility in the 2d Ising model, in great detail with very little
computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references
added and minor changes of style. vs3: Corrections made and reference adde
Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models
We study the q-dependent susceptibility chi(q) of a series of quasiperiodic
Ising models on the square lattice. Several different kinds of aperiodic
sequences of couplings are studied, including the Fibonacci and silver-mean
sequences. Some identities and theorems are generalized and simpler derivations
are presented. We find that the q-dependent susceptibilities are periodic, with
the commensurate peaks of chi(q) located at the same positions as for the
regular Ising models. Hence, incommensurate everywhere-dense peaks can only
occur in cases with mixed ferromagnetic-antiferromagnetic interactions or if
the underlying lattice is aperiodic. For mixed-interaction models the positions
of the peaks depend strongly on the aperiodic sequence chosen.Comment: LaTeX2e, 26 pages, 9 figures (27 eps files). v2: Misprints correcte
Correlation functions for the three state superintegrable chiral Potts spin chain of finite lengths
We compute the correlation functions of the three state superintegrable
chiral Potts spin chain for chains of length 3,4,5. From these results we
present conjectures for the form of the nearest neighbor correlation function.Comment: 10 pages; references update
Long-Time Tails and Anomalous Slowing Down in the Relaxation of Spatially Inhomogeneous Excitations in Quantum Spin Chains
Exact analytic calculations in spin-1/2 XY chains, show the presence of
long-time tails in the asymptotic dynamics of spatially inhomogeneous
excitations. The decay of inhomogeneities, for , is given in the
form of a power law where the relaxation time
and the exponent depend on the wave vector ,
characterizing the spatial modulation of the initial excitation. We consider
several variants of the XY model (dimerized, with staggered magnetic field,
with bond alternation, and with isotropic and uniform interactions), that are
grouped into two families, whether the energy spectrum has a gap or not. Once
the initial condition is given, the non-equilibrium problem for the
magnetization is solved in closed form, without any other assumption. The
long-time behavior for can be obtained systematically in a form
of an asymptotic series through the stationary phase method. We found that
gapped models show critical behavior with respect to , in the sense that
there exist critical values , where the relaxation time
diverges and the exponent changes discontinuously. At those points, a
slowing down of the relaxation process is induced, similarly to phenomena
occurring near phase transitions. Long-lived excitations are identified as
incommensurate spin density waves that emerge in systems undergoing the Peierls
transition. In contrast, gapless models do not present the above anomalies as a
function of the wave vector .Comment: 25 pages, 2 postscript figures. Manuscript submitted to Physical
Review
Factorized finite-size Ising model spin matrix elements from Separation of Variables
Using the Sklyanin-Kharchev-Lebedev method of Separation of Variables adapted
to the cyclic Baxter--Bazhanov--Stroganov or -model, we derive
factorized formulae for general finite-size Ising model spin matrix elements,
proving a recent conjecture by Bugrij and Lisovyy
Transthoracic echocardiography performed by intensive care fellows: is minimal focused training enough?
Eigenvectors in the Superintegrable Model I: sl_2 Generators
In order to calculate correlation functions of the chiral Potts model, one
only needs to study the eigenvectors of the superintegrable model. Here we
start this study by looking for eigenvectors of the transfer matrix of the
periodic tau_2(t)model which commutes with the chiral Potts transfer matrix. We
show that the degeneracy of the eigenspace of tau_2(t) in the Q=0 sector is
2^r, with r=(N-1)L/N when the size of the transfer matrix L is a multiple of N.
We introduce chiral Potts model operators, different from the more commonly
used generators of quantum group U-tilde_q(sl-hat(2)). From these we can form
the generators of a loop algebra L(sl(2)). For this algebra, we then use the
roots of the Drinfeld polynomial to give new explicit expressions for the
generators representing the loop algebra as the direct sum of r copies of the
simple algebra sl(2).Comment: LaTeX 2E document, 11 pages, 1 eps figure, using iopart.cls with
graphicx and iopams packages. v2: Appended text to title, added
acknowledgments and made several minor corrections v3: Added reference,
eliminated ambiguity, corrected a few misprint
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