Statistical Physics of Disordered Systems:
A Celebration in Honor of Dan Stein's 60th Birthday


Thursday, August 22, 2013
8:15AMBreakfast: Coffee/Juice/Muffins/Bagels, 13th Floor Commons
9:00AM Welcome/Introductory Remarks
9:15AM Tom Rosenbaum
University of Chicago

Quantum Spin Glasses

10:00AM Alan Middleton
Syracuse University

Which Measures of Spin Glass Overlaps are Informative? Reports from Flatland

10:45AM Coffee Break, 13th Floor Commons
11:15AM Mike Moore
University of Manchester

The Almeida-Thouless Line in Spin Glasses

For nearly 30 years an argument has raged as to the nature of the low-temperature phase of spin glasses. There are two main theories. The first is the theory of Parisi which is based upon the idea that the ordered phase is like that found in mean-field theory: it has a large number of pure states arranged in an ultrametric topology and has broken replica symmetry, (RSB). For finite dimensional systems Newman and Stein have modified this picture to the chaotic pair state. The other theory is that of the droplet model which is based on simple scaling and renormalization group ideas and has but two pure states, (just as in a ferromagnet). The low-temperature phase has replica symmetry.
According to RSB theory there is a phase transition line, the de Almeida-Thouless (AT) line, when a field is applied to the spin glass. At temperature above the line there is the replica symmetric paramagnetic phase. Below it there is a phase with RSB. However, according to the droplet picture there is no phase transition at all in the presence of a field, just as for a ferromagnet whose phase transition is removed by a field. A huge effort has been made by experimentalists and simulators to find if there is such a phase transition line. Some of this work will be reviewed but unfortunately the conclusions to be drawn from these studies remains controversial.
In my talk I shall list arguments that the AT line exists in more than six dimensions: that is, RSB applies only when the dimensionality d > 6. These results derive from RG ideas and from a 1/m expansion of the m-component spin glass model.
Next I will turn to simulations. In recent years it has been realized that one can learn a lot about d-dimensional spin glass models by studying the one-dimensional spin glass model with long-range interactions introduced by Kotliar, Anderson and Stein, where the interactions between spins decrease with their separation Rij as 1/Rijσ. The mapping between σ and d will be explained. Simulations which indicate for what range of σ there might be an AT line will be outlined. The controversy between different simulators will be discussed.

12:00PM Phil Anderson
Princeton University

Remarks on Supersolidity

12:45PM Lunch, 13th Floor Commons
2:15PM Charles Doering
University of Michigan

Features of Fast Living: On the Weak Selection for Longevity in Degenerate Birth-Death Processes

Deterministic descriptions of the dynamics of competing species with identical carrying capacities but distinct birth, death, and reproduction rates predict steady state coexistence with population ratios depending on initial conditions. Demographic fluctuations described by a Markovian birth-death model break this degeneracy. A novel large carrying capacity asymptotic theory confirmed by conventional analysis and simulations reveals a weak preference for longevity in the deterministic limit with finite-time extinction of one of the competitors on a time scale proportional to the total carrying capacity.

3:00PM Mark Dykman
Michigan State University

Fragility of the Rates of Rare Events

We discuss rare events that result from large classical and quantum fluctuations in systems away from thermal equilibrium. They include switching between coexisting stable states in dynamical systems and population (species) extinction in population dynamics and chemical systems. We show that the rates of rare events can discontinuously change with the change of the parameters of the system. Using examples of currently studied physical systems, we discuss the criteria for the onset of fragility, the discontinuous change of the most probable paths followed in rare events, and the associated modification of the conventional analysis of the rates of rare events. This talk is dedicated to Dan Stein, who made an outstanding contribution to the theory of rare events.

3:45PM Coffee Break, 13th Floor Commons
4:15PM Michael Damron
Indiana University

Broken Ergodicity and Invasion Percolation

5:00PM Robert Austin
Princeton University

The Joys of Being Young and Doomed at Princeton

5:45PM Closing Remarks
6:00PM End of First Day
6:45PM Gala Dinner at Legends Restaurant , 88 7th Avenue, between 15th and 16th Street
Friday, August 23, 2013
8:15AMBreakfast: Coffee/Juice/Muffins/Bagels, 13th Floor Commons
9:00AM Introductory Remarks
9:15AM Daniel Fisher
Stanford University

Randomness and Evolutionary Dynamics

10:00AM Marija Vucelja
New York University

Insights from Spin-Glasses in Population Genetics: Emergence of Clones in Populations

Population genetics studies how genes and alleles evolve. It is a very important subject and an active field of research. A deep theoretical understanding of population genetics is essential for describing many biological phenomena, and for explaining the genetic diversity that we observe. From the standpoint of physics population genetics represents a complex, interacting, non-equilibrium statistical physics problem and as such is quite challenging, and in many cases yet unsolved and puzzling. My talk is about the emergence of large clones in populations. Clones arise in cases where the selection managed to amplify individual genotypes in spite evolutionary processes that aim to reshuffle the genetic material (recombinations and mutations). The "clonal condensation" is an essential phenomenon, present in many populations, that has not been captured by traditional population genetics measures (such as linkage disequilibrium). I will point out the similarity between the clonal condensation and the freezing transition in the Random Energy Model of spin glasses. Guided by this analogy I will derive one of the key quantities of interest: the probability that two individuals are genetically identical. This quantity is the analog of the spin-glass order parameter, and it is also closely related to rate of coalescence in population genetics: two individuals that come from the same clone have a recent common ancestor. I will summarize of the present understanding of this condensation phenomena. Finally, I will describe future directions in population genetics, linking physics and biology closer together.

10:45AM Coffee Break, 13th Floor Commons
11:15AM James Sauls
Northwestern University

Chiral Superfluid Order in an Anisotropic Glass

Random fields coupled to an order parameter describing one or more broken continuous symmetries have been investigated since the early 1970’s - from the destruction of long-range order of the Abrikosov vortex lattice in type II superconductor to ferromagnetism in a materials random magnetic disorder. In this talk I argue that the quantum liquid phases of 3He infused into silica aerogel provide a unique system for studying the struggle between orbital order of Cooper pairs, and disorder characterized by random anisotropy. This competition leads to remarkable new chiral superfluid phases exhibiting broken time-inversion symmetry, space parity, and as I argue, a novel phase that has finite range orientational order in two dimensions, but long range order in a third dimension. This phase is the realization of a biaxial-chiral phase with finite-range orientational correlations due to the random anisotropy field of the aerogel medium. These conclusions are sup- ported by theoretical analysis of the phase diagram and NMR spectra of superfluid 3He infused into anisotropic aerogel.

12:00PM Charles Stafford
University of Arizona

Probing Maxwell's Demon with a Nanoscale Thermometer

Recent advances in thermal microscopy, where spatial and thermal resolutions of 10nm and 15mK, respectively, have been achieved,1 raise a fundamental question, “On how short a length scale can a statistical quantity like temperature be meaningfully defined?” We tackle this question theoretically2 by first providing a physically motivated and mathematically rigorous definition of an electron thermometer as an open third terminal in a thermoelectric circuit. We then develop a realistic model of a scanning thermal microscope (SThM) with atomic resolution, operating in the tunneling regime in ultrahigh vacuum, including the thermal coupling of the probe to the ambient environment. With this model of an electron thermometer, we investigate the temperature distributions in molecular junctions,2 and graphene nanoribbons3 under thermal bias. We find that the temperatures of individual atomic orbitals (or bonds) in these systems exhibit quantum oscillations; quantum interference mimics the actions of a Maxwell Demon, allowing electrons from the hot electrode to tunnel onto the temperature probe when it is at certain locations near the molecule, and blocking electrons from the cold electrode, or vice versa. A crossover to a classical temperature distribution consistent with Fourier’s law of heat conduction is predicted as the spatial resolution of the temperature probe is reduced.

1Kim, K.; Jeong, W.; Lee, W.; Reddy, P. “Ultra-High Vacuum Scanning Thermal Microscopy for Nanometer Resolution Quantitative Thermometry,” ACS Nano 6, 4248–4257 (2012).
2Justin P. Bergfield, Shauna M. Story, Robert C. Stafford, Charles A. Stafford, “Probing Maxwell's Demon with a Nanoscale Thermometer,” ACS Nano 7, 4429-4440 (2013).
3Justin P. Bergfield, Mark A. Ratner, Charles A. Stafford, Massimiliano Di Ventra, “Tunable Quantum Temperature Oscillations in Graphene and Carbon Nanoribbons,” arXiv:1305.6602.

12:45PM Lunch, 13th Floor Commons
2:15PM Louis-Pierre Arguin
University of Montreal

The Mathematics of Short-range Spin Glasses: Some Proofs and (Many) Open Problems

The rigorous understanding of the structure of mean-field spin glass models have undergone tremendous progress in the last fifteen years. This is to be compared with the finite-dimensional models where many questions remain open. In this talk, I will survey results on short-range spin glasses that were obtained by Dan Stein and collaborators over the years that aim to answer some of these questions and to shed light on the low-temperature behavior of these models.

3:00PM Pierluigi Contucci
University of Bologna

Quenched Diluted Models with Hardcore Interactions

The seminar will introduce the quenched diluted models of monomer-dimer type. The deterministic case and its properties, solved by Heilmann and Lieb, will be reviewed. The diluted version exact formula, found within the replica symmetric cavity approach, will be rigorously proven. The model turns out to have an analytic pressure whose monomer density is explicitly identified by the expectation of the solution of a fixed point distributional equation. Joint work with Diego Alberici.

3:45PM Gerard Ben-Arous
New York University

Randomly Trapped Random Walks

I will describe a very general scheme of trapping for random walks on graphs, which contains the usual Fractional Kinetics or Bouchaud Trap models as simple examples. A full study of their possible scaling limits in dimension 1 will be given. This will be applied to the case of the scaling limit of the RW on incipient infinite cluster on critical trees, and on invasion percolation clusters on trees. This work was started long ago in the PhD thesis of Roman Royfman and has been completed only recently in a joint work with Jiri Cerny and Manuel Cabezas.

4:30PM Conclusion
4:45PM Closing Reception, 13th Floor Commons