505 research outputs found
Critical Droplets and Phase Transitions in Two Dimensions
In two space dimensions, the percolation point of the pure-site clusters of
the Ising model coincides with the critical point T_c of the thermal transition
and the percolation exponents belong to a special universality class. By
introducing a bond probability p_B<1, the corresponding site-bond clusters keep
on percolating at T_c and the exponents do not change, until
p_B=p_CK=1-exp(-2J/kT): for this special expression of the bond weight the
critical percolation exponents switch to the 2D Ising universality class. We
show here that the result is valid for a wide class of bidimensional models
with a continuous magnetization transition: there is a critical bond
probability p_c such that, for any p_B>=p_c, the onset of percolation of the
site-bond clusters coincides with the critical point of the thermal transition.
The percolation exponents are the same for p_c<p_B<=1 but, for p_B=p_c, they
suddenly change to the thermal exponents, so that the corresponding clusters
are critical droplets of the phase transition. Our result is based on Monte
Carlo simulations of various systems near criticality.Comment: Final version for publication, minor changes, figures adde
To claim or not to claim
Verslag van een themabijeenkomst welke als doel had om de sector concrete handvatten aan te reiken voor het aanvragen én realiseren van een gezondheidsclaim
Lebowitz Inequalities for Ashkin-Teller Systems
We consider the Ashkin-Teller model with negative four-spin coupling but
still in the region where the ground state is ferromagnetic. We establish the
standard Lebowitz inequality as well as the extension that is necessary to
prove a divergent susceptibility.Comment: Ams-TeX, 12 pages; two references added, final version accepted for
publication in Physica
Exact sampling from non-attractive distributions using summary states
Propp and Wilson's method of coupling from the past allows one to efficiently
generate exact samples from attractive statistical distributions (e.g., the
ferromagnetic Ising model). This method may be generalized to non-attractive
distributions by the use of summary states, as first described by Huber. Using
this method, we present exact samples from a frustrated antiferromagnetic
triangular Ising model and the antiferromagnetic q=3 Potts model. We discuss
the advantages and limitations of the method of summary states for practical
sampling, paying particular attention to the slowing down of the algorithm at
low temperature. In particular, we show that such a slowing down can occur in
the absence of a physical phase transition.Comment: 5 pages, 6 EPS figures, REVTeX; additional information at
http://wol.ra.phy.cam.ac.uk/mackay/exac
Rejection-free Geometric Cluster Algorithm for Complex Fluids
We present a novel, generally applicable Monte Carlo algorithm for the
simulation of fluid systems. Geometric transformations are used to identify
clusters of particles in such a manner that every cluster move is accepted,
irrespective of the nature of the pair interactions. The rejection-free and
non-local nature of the algorithm make it particularly suitable for the
efficient simulation of complex fluids with components of widely varying size,
such as colloidal mixtures. Compared to conventional simulation algorithms,
typical efficiency improvements amount to several orders of magnitude
On Spin Systems with Quenched Randomness: Classical and Quantum
The rounding of first order phase transitions by quenched randomness is
stated in a form which is applicable to both classical and quantum systems: The
free energy, as well as the ground state energy, of a spin system on a
-dimensional lattice is continuously differentiable with respect to any
parameter in the Hamiltonian to which some randomness has been added when . This implies absence of jumps in the associated order parameter, e.g.,
the magnetization in case of a random magnetic field. A similar result applies
in cases of continuous symmetry breaking for . Some questions
concerning the behavior of related order parameters in such random systems are
discussed.Comment: 8 pages LaTeX, 2 PDF figures. Presented by JLL at the symposium
"Trajectories and Friends" in honor of Nihat Berker, MIT, October 200
Microcanonical cluster algorithms
I propose a numerical simulation algorithm for statistical systems which
combines a microcanonical transfer of energy with global changes in clusters of
spins. The advantages of the cluster approach near a critical point augment the
speed increases associated with multi-spin coding in the microcanonical
approach. The method also provides a limited ability to tune the average
cluster size.Comment: 10 page
Quark Matter and Nuclear Collisions: A Brief History of Strong Interaction Thermodynamics
The past fifty years have seen the emergence of a new field of research in
physics, the study of matter at extreme temperatures and densities. The theory
of strong interactions, quantum chromodynamics (QCD), predicts that in this
limit, matter will become a plasma of deconfined quarks and gluons -- the
medium which made up the early universe in the first 10 microseconds after the
big bang. High energy nuclear collisions are expected to produce short-lived
bubbles of such a medium in the laboratory. I survey the merger of statistical
QCD and nuclear collision studies for the analysis of strongly interacting
matter in theory and experiment.Comment: 24 pages, 14 figures Opening Talk at the 5th Berkeley School on
Collective Dynamics in High Energy Collisions, LBNL Berkeley/California, May
14 - 18, 201
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