33 research outputs found
Bethe ansatz solution of zero-range process with nonuniform stationary state
The eigenfunctions and eigenvalues of the master-equation for zero range
process with totally asymmetric dynamics on a ring are found exactly using the
Bethe ansatz weighted with the stationary weights of particle configurations.
The Bethe ansatz applicability requires the rates of hopping of particles out
of a site to be the -numbers . This is a generalization of the rates
of hopping of noninteracting particles equal to the occupation number of a
site of departure. The noninteracting case can be restored in the limit . The limiting cases of the model for correspond to the totally
asymmetric exclusion process, and the drop-push model respectively. We analyze
the partition function of the model and apply the Bethe ansatz to evaluate the
generating function of the total distance travelled by particles at large time
in the scaling limit. In case of non-zero interaction, , the
generating function has the universal scaling form specific for the
Kardar-Parizi-Zhang universality class.Comment: 7 pages, Revtex4, mistypes correcte
Equilibrium shapes and faceting for ionic crystals of body-centered-cubic type
A mean field theory is developed for the calculation of the surface free
energy of the staggered BCSOS, (or six vertex) model as function of the surface
orientation and of temperature. The model approximately describes surfaces of
crystals with nearest neighbor attractions and next nearest neighbor
repulsions. The mean field free energy is calculated by expressing the model in
terms of interacting directed walks on a lattice. The resulting equilibrium
shape is very rich with facet boundaries and boundaries between reconstructed
and unreconstructed regions which can be either sharp (first order) or smooth
(continuous). In addition there are tricritical points where a smooth boundary
changes into a sharp one and triple points where three sharp boundaries meet.
Finally our numerical results strongly suggest the existence of conical points,
at which tangent planes of a finite range of orientations all intersect each
other. The thermal evolution of the equilibrium shape in this model shows
strong similarity to that seen experimentally for ionic crystals.Comment: 14 Pages, Revtex and 10 PostScript figures include
Asymmetric XXZ chain at the antiferromagnetic transition: Spectra and partition functions
The Bethe ansatz equation is solved to obtain analytically the leading
finite-size correction of the spectra of the asymmetric XXZ chain and the
accompanying isotropic 6-vertex model near the antiferromagnetic phase boundary
at zero vertical field. The energy gaps scale with size as and
its amplitudes are obtained in terms of level-dependent scaling functions.
Exactly on the phase boundary, the amplitudes are proportional to a sum of
square-root of integers and an anomaly term. By summing over all low-lying
levels, the partition functions are obtained explicitly. Similar analysis is
performed also at the phase boundary of zero horizontal field in which case the
energy gaps scale as . The partition functions for this case are found
to be that of a nonrelativistic free fermion system. From symmetry of the
lattice model under rotation, several identities between the partition
functions are found. The scaling at zero vertical field is
interpreted as a feature arising from viewing the Pokrovsky-Talapov transition
with the space and time coordinates interchanged.Comment: Minor corrections only. 18 pages in RevTex, 2 PS figure
Extended Universality of the Surface Curvature in Equilibrium Crystal Shapes
We investigate the universal property of curvatures in surface models which
display a flat phase and a rough phase whose criticality is described by the
Gaussian model. Earlier we derived a relation between the Hessian of the free
energy and the Gaussian coupling constant in the six-vertex model. Here we show
its validity in a general setting using renormalization group arguments. The
general validity of the relation is confirmed numerically in the RSOS model by
comparing the Hessian of the free energy and the Gaussian coupling constant in
a transfer matrix finite-size-scaling study. The Hessian relation gives clear
understanding of the universal curvature jump at roughening transitions and
facet edges and also provides an efficient way of locating the phase
boundaries.Comment: 19 pages, RevTex, 3 Postscript Figures, To appear in Phys. Rev.
The Conical Point in the Ferroelectric Six-Vertex Model
We examine the last unexplored regime of the asymmetric six-vertex model: the
low-temperature phase of the so-called ferroelectric model. The original
publication of the exact solution, by Sutherland, Yang, and Yang, and various
derivations and reviews published afterwards, do not contain many details about
this regime. We study the exact solution for this model, by numerical and
analytical methods. In particular, we examine the behavior of the model in the
vicinity of an unusual coexistence point that we call the ``conical'' point.
This point corresponds to additional singularities in the free energy that were
not discussed in the original solution. We show analytically that in this point
many polarizations coexist, and that unusual scaling properties hold in its
vicinity.Comment: 28 pages (LaTeX); 8 postscript figures available on request
([email protected]). Submitted to Journal of Statistical Physics. SFU-DJBJDS-94-0
Phase Separation of Crystal Surfaces: A Lattice Gas Approach
We consider both equilibrium and kinetic aspects of the phase separation
(``thermal faceting") of thermodynamically unstable crystal surfaces into a
hill--valley structure. The model we study is an Ising lattice gas for a simple
cubic crystal with nearest--neighbor attractive interactions and weak
next--nearest--neighbor repulsive interactions. It is likely applicable to
alkali halides with the sodium chloride structure. Emphasis is placed on the
fact that the equilibrium crystal shape can be interpreted as a phase diagram
and that the details of its structure tell us into which surface orientations
an unstable surface will decompose. We find that, depending on the temperature
and growth conditions, a number of interesting behaviors are expected. For a
crystal in equilibrium with its vapor, these include a low temperature regime
with logarithmically--slow separation into three symmetrically--equivalent
facets, and a higher temperature regime where separation proceeds as a power
law in time into an entire one--parameter family of surface orientations. For a
crystal slightly out of equilibrium with its vapor (slow crystal growth or
etching), power--law growth should be the rule at late enough times. However,
in the low temperature regime, the rate of separation rapidly decreases as the
chemical potential difference between crystal and vapor phases goes to zero.Comment: 16 pages (RevTex 3.0); 12 postscript figures available on request
([email protected]). Submitted to Physical Review E. SFU-JDSDJB-94-0
Charge Frustration Effects in Capacitively Coupled Two-Dimensional Josephson-Junction Arrays
We investigate the quantum phase transitions in two capacitively coupled
two-dimensional Josephson-junction arrays with charge frustration. The system
is mapped onto the S=1 and anisotropic Heisenberg antiferromagnets near
the particle-hole symmetry line and near the maximal-frustration line,
respectively, which are in turn argued to be effectively described by a single
quantum phase model. Based on the resulting model, it is suggested that near
the maximal frustration line the system may undergo a quantum phase transition
from the charge-density wave to the super-solid phase, which displays both
diagonal and off- diagonal long-range order.Comment: 6 pages, 6 figures, to appear in Phys. Rev.
Formation and Interaction of Membrane Tubes
We show that the formation of membrane tubes (or membrane tethers), which is
a crucial step in many biological processes, is highly non-trivial and involves
first order shape transitions. The force exerted by an emerging tube is a
non-monotonic function of its length. We point out that tubes attract each
other, which eventually leads to their coalescence. We also show that detached
tubes behave like semiflexible filaments with a rather short persistence
length. We suggest that these properties play an important role in the
formation and structure of tubular organelles.Comment: 4 pages, 3 figure
Finite-size scaling and the toroidal partition function of the critical asymmetric six-vertex model
Finite-size corrections to the energy levels of the asymmetric six-vertex
model transfer matrix are considered using the Bethe ansatz solution for the
critical region. The non-universal complex anisotropy factor is related to the
bulk susceptibilities. The universal Gaussian coupling constant is also
related to the bulk susceptibilities as , being the
Hessian of the bulk free energy surface viewed as a function of the two fields.
The modular covariant toroidal partition function is derived in the form of the
modified Coulombic partition function which embodies the effect of
incommensurability through two mismatch parameters. The effect of twisted
boundary conditions is also considered.Comment: 19 pages, 5 Postscript figure files in the form of uuencoded
compressed tar fil
Professor C. N. Yang and Statistical Mechanics
Professor Chen Ning Yang has made seminal and influential contributions in
many different areas in theoretical physics. This talk focuses on his
contributions in statistical mechanics, a field in which Professor Yang has
held a continual interest for over sixty years. His Master's thesis was on a
theory of binary alloys with multi-site interactions, some 30 years before
others studied the problem. Likewise, his other works opened the door and led
to subsequent developments in many areas of modern day statistical mechanics
and mathematical physics. He made seminal contributions in a wide array of
topics, ranging from the fundamental theory of phase transitions, the Ising
model, Heisenberg spin chains, lattice models, and the Yang-Baxter equation, to
the emergence of Yangian in quantum groups. These topics and their
ramifications will be discussed in this talk.Comment: Talk given at Symposium in honor of Professor C. N. Yang's 85th
birthday, Nanyang Technological University, Singapore, November 200