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 $d$-dimensional lattice is continuously differentiable with respect to any parameter in the Hamiltonian to which some randomness has been added when $d \leq 2$. 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 $d \leq 4$. 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

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

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