78 research outputs found
Ensemble dependence in the Random transverse-field Ising chain
In a disordered system one can either consider a microcanonical ensemble,
where there is a precise constraint on the random variables, or a canonical
ensemble where the variables are chosen according to a distribution without
constraints. We address the question as to whether critical exponents in these
two cases can differ through a detailed study of the random transverse-field
Ising chain. We find that the exponents are the same in both ensembles, though
some critical amplitudes vanish in the microcanonical ensemble for correlations
which span the whole system and are particularly sensitive to the constraint.
This can \textit{appear} as a different exponent. We expect that this apparent
dependence of exponents on ensemble is related to the integrability of the
model, and would not occur in non-integrable models.Comment: 8 pages, 12 figure
Cluster Monte Carlo study of multi-component fluids of the Stillinger-Helfand and Widom-Rowlinson type
Phase transitions of fluid mixtures of the type introduced by Stillinger and
Helfand are studied using a continuum version of the invaded cluster algorithm.
Particles of the same species do not interact, but particles of different types
interact with each other via a repulsive potential. Examples of interactions
include the Gaussian molecule potential and a repulsive step potential.
Accurate values of the critical density, fugacity and magnetic exponent are
found in two and three dimensions for the two-species model. The effect of
varying the number of species and of introducing quenched impurities is also
investigated. In all the cases studied, mixtures of -species are found to
have properties similar to -state Potts models.Comment: 25 pages, 5 figure
Surface tension in the dilute Ising model. The Wulff construction
We study the surface tension and the phenomenon of phase coexistence for the
Ising model on \mathbbm{Z}^d () with ferromagnetic but random
couplings. We prove the convergence in probability (with respect to random
couplings) of surface tension and analyze its large deviations : upper
deviations occur at volume order while lower deviations occur at surface order.
We study the asymptotics of surface tension at low temperatures and relate the
quenched value of surface tension to maximal flows (first passage
times if ). For a broad class of distributions of the couplings we show
that the inequality -- where is the surface
tension under the averaged Gibbs measure -- is strict at low temperatures. We
also describe the phenomenon of phase coexistence in the dilute Ising model and
discuss some of the consequences of the media randomness. All of our results
hold as well for the dilute Potts and random cluster models
Determination of the order of phase transitions in Potts model by the graph-weight approach
We examine the order of the phase transition in the Potts model by using the
graph representation for the partition function, which allows treating a
non-integer number of Potts states. The order of transition is determined by
the analysis of the shape of the graph-weight probability distribution. The
approach is illustrated on special cases of the one-dimensional Potts model
with long-range interactions and on its mean-field limit.Comment: 12 pages LaTeX, 2 eps figures; to be published in Physica
Outlets of 2D invasion percolation and multiple-armed incipient infinite clusters
We study invasion percolation in two dimensions, focusing on properties of
the outlets of the invasion and their relation to critical percolation and to
incipient infinite clusters (IIC's). First we compute the exact decay rate of
the distribution of both the weight of the kth outlet and the volume of the kth
pond. Next we prove bounds for all moments of the distribution of the number of
outlets in an annulus. This result leads to almost sure bounds for the number
of outlets in a box B(2^n) and for the decay rate of the weight of the kth
outlet to p_c. We then prove existence of multiple-armed IIC measures for any
number of arms and for any color sequence which is alternating or
monochromatic. We use these measures to study the invaded region near outlets
and near edges in the invasion backbone far from the origin.Comment: 38 pages, 10 figures, added a thorough sketch of the proof of
existence of IIC's with alternating or monochromatic arms (with some
generalizations
Competition between fluctuations and disorder in frustrated magnets
We investigate the effects of impurities on the nature of the phase
transition in frustrated magnets, in d=4-epsilon dimensions. For sufficiently
small values of the number of spin components, we find no physically relevant
stable fixed point in the deep perturbative region (epsilon << 1), contrarily
to what is to be expected on very general grounds. This signals the onset of
important physical effects.Comment: 4 pages, 3 figures, published versio
On Random Field Induced Ordering in the Classical XY Model
Consider the classical XY model in a weak random external field pointing
along the axis with strength . We study the behavior of this
model as the range of the interaction is varied. We prove that in any dimension
and for all sufficiently small, there is a range
so that whenever the inverse temperature is larger than
some , there is strong residual ordering along the
direction.Comment: 30 page
Anomalous Quantum Diffusion at the Superfluid-Insulator Transition
We consider the problem of the superconductor-insulator transition in the
presence of disorder, assuming that the fermionic degrees of freedom can be
ignored so that the problem reduces to one of Cooper pair localization. Weak
disorder drives the critical behavior away from the pure critical point,
initially towards a diffusive fixed point. We consider the effects of Coulomb
interactions and quantum interference at this diffusive fixed point. Coulomb
interactions enhance the conductivity, in contrast to the situation for
fermions, essentially because the exchange interaction is opposite in sign. The
interaction-driven enhancement of the conductivity is larger than the
weak-localization suppression, so the system scales to a perfect conductor.
Thus, it is a consistent possibility for the critical resistivity at the
superconductor-insulator transition to be zero, but this value is only
approached logarithmically. We determine the values of the critical exponents
and comment on possible implications for the interpretation of
experiments
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