Partition Function Zeros at First-Order Phase Transitions: A General Analysis

We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a companion paper [5]. Under these assumptions, we derive equations whose solutions give the location of the zeros of the partition function with periodic boundary conditions, up to an error which we prove is (generically) exponentially small in the linear size of the system. For asymptotically large systems, the zeros concentrate on phase boundaries which are simple curves ending in multiple points. For models with an Ising-like plus-minus symmetry, we also establish a local version of the Lee-Yang Circle Theorem. This result allows us to control situations when in one region of the complex plane the zeros lie precisely on the unit circle, while in the complement of this region the zeros concentrate on less symmetric curves.Reproduction of the entire article for non-commercial purposes is permitted without charge.     

Partition Function Zeros at First-Order Phase Transitions: Pirogov—Sinai Theory

This paper is a continuation of our previous analysis(2) of partition functions zeros in models with first-order phase transitions and periodic boundary conditions. Here it is shown that the assumptions under which the results of ref. 2 were established are satisfied by a large class of lattice models. These models are characterized by two basic properties: The existence of only a finite number of ground states and the availability of an appropriate contour representation. This setting includes, for instance, the Ising, Potts, and Blume–Capel models at low temperatures. The combined results of ref. 2 and the present paper provide complete control of the zeros of the partition function with periodic boundary conditions for all models in the above class.     

A Proof of the Gibbs—Thomson Formula in the Droplet Formation Regime

We study equilibrium droplets in two-phase systems at parameter values corresponding to phase coexistence. Specifically, we give a self-contained microscopic derivation of the Gibbs–Thomson formula for the deviation of the pressure and the density away from their equilibrium values which, according to the interpretation of the classical thermodynamics, appears due to the presence of a curved interface. The general—albeit heuristic—reasoning is corroborated by a rigorous proof in the case of the two-dimensional Ising lattice gas.     

Limit theory for random walks in degenerate time-dependent random environments

We study continuous-time (variable speed) random walks in random environments on ${\mathbb{Z}}^d$, $d\ge 2$, where, at time t, the walk at x jumps across edge $(x,y)$ at time-dependent rate $a_t(x,y)$. The rates, which we assume stationary and ergodic with respect to space–time shifts, are symmetric and bounded but possibly degenerate in the sense that the total jump rate from a vertex may vanish over finite intervals of time. We formulate conditions on the environment under which the law of diffusively-scaled random walk path tends to Brownian motion for almost every sample of the rates. The proofs invoke Moser iteration to prove sublinearity of the corrector in pointwise sense; a key additional input is a conversion of certain weighted energy norms to ordinary ones. Our conclusions apply to random walks on dynamical bond percolation and interacting particle systems as well as to random walks arising from the Helffer–Sjöstrand representation of gradient models with certain non-strictly convex potentials.     

First Synthesis of Highly Chemiluminescent Benzo[b]furan‐2(3H)‐ones Bearing a Urea Substructure

A series of benzo[b]furan‐2(3H)‐ones (coumaran‐2‐ones) bearing a urea substructure, namely derivatives of 3‐(aminocarbonylamino)benzo[b]furan‐2(3H)‐one, was prepared for the first time. The accessibility of these compounds through an electrophilic α‐amidoalkylation approach of phenols (Tscherniac–Einhorn reaction) in the key step as well as the chemiluminescence (CL) properties of the desired compounds are strongly dependent on the substitution patterns at the urea moiety. Competing reaction pathways are discussed and an improved one pot synthetical approach of also general interest is presented. In conclusion, especially N,N‐dialkylaminocarbonylamino‐derivatives of benzo[b]furan‐2(3H)‐ones exhibit a strong flash like blue CL upon treatment with bases such as 1,8‐diazabicyclo[5.4.0]undec‐7‐ene (DBU) in the presence of oxygen or hydrogen peroxide. Comparative physico‐chemical investigations revealed that novel compounds outperform their urethane‐analogues in terms of CL‐intensity and the speed of the decay making them potentially useful as new tools for CL‐based applications on the short time scale.     

Screening Effect Due to Heavy Lower Tails in One-Dimensional Parabolic Anderson Model

We consider the large-time behavior of the solution to the parabolic Anderson problem _tu=u+u with initial data u(0, ·)=1 and non-positive finite i.i.d. potentials . Unlike in dimensions d2, the almost-sure decay rate of u(t, 0) as t is not determined solely by the upper tails of (0); too heavy lower tails of (0) accelerate the decay. The interpretation is that sites x with large negative (x) hamper the mass flow and hence screen off the influence of more favorable regions of the potential. The phenomenon is unique to d=1. The result answers an open question from our previous study [BK00] of this model in general dimension.     

Phase transition and critical behavior in a model of organized criticality

We study a model of organized criticality, where a single avalanche propagates through an a priori static (i.e., organized) sandpile configuration. The latter is chosen according to an i.i.d. distribution from a Borel probability measure on [0,1]. The avalanche dynamics is driven by a standard toppling rule, however, we simplify the geometry by placing the problem on a directed, rooted tree. As our main result, we characterize which are critical in the sense that they do not admit an infinite avalanche but exhibit a power-law decay of avalanche sizes. Our analysis reveals close connections to directed site-percolation, both in the characterization of criticality and in the values of the critical exponents.Mathematics Subject Classification (2000): 60K35, 82C20, 82C44     

Time-resolved electron paramagnetic resonance of radical pair intermediates in cryptochromes

Electron transfer plays a key role in many biological systems, including core complexes of photosynthesis and respiration. As this involves unpaired electron spins, electron paramagnetic resonance (EPR) is the method of choice to investigate such processes. Systems that show photo-induced charge separation and electron transfer are of particular interest, as here the processes can easily be synchronised to the experiment and therefore followed directly over its time course. One particular class of proteins, the cryptochromes, showing charge separation and in turn spin-correlated radical pairs upon excitation with blue light, have been investigated by time-resolved EPR spectroscopy in great detail and the results obtained so far are summarised in this contribution. Highlights include the first observation of spin-correlated radical pairs in these proteins, a fact with great impact on the proposed role as key part of a magnetic compass of migratory birds, as well as the assignment of the radical-pair partners and the unravelling of alternative and unexpected electron transfer pathways in these proteins, giving new insights into aspects of biological electron transfer itself.