Rigorous Analysis of Singularities and Absence of Analytic Continuation at First Order Phase Transition Points in Lattice Spin Models

We report about two new rigorous results on the non-analytic properties of thermodynamic potentials at first order phase transition. The first one is valid for lattice models ($d\geq 2$) with arbitrary finite state space, and finite-range interactions which have two ground states. Under the only assumption that the Peierls Condition is satisfied for the ground states and that the temperature is sufficiently low, we prove that the pressure has no analytic continuation at the first order phase transition point. The second result concerns Ising spins with Kac potentials $J_\gamma(x)=\gamma^d\phi(\gamma x)$, where $0<\gamma<1$ is a small scaling parameter, and $\phi$ a fixed finite range potential. In this framework, we relate the non-analytic behaviour of the pressure at the transition point to the range of interaction, which equals $\gamma^{-1}$. Our analysis exhibits a crossover between the non-analytic behaviour of finite range models ($\gamma>0$) and analyticity in the mean field limit ($\gamma\searrow 0$). In general, the basic mechanism responsible for the appearance of a singularity blocking the analytic continuation is that arbitrarily large droplets of the other phase become stable at the transition point.Comment: 4 pages, 2 figure

Mean-field driven first-order phase transitions in systems with long-range interactions

We consider a class of spin systems on $\Z^d$ with vector valued spins (\bS_x) that interact via the pair-potentials J_{x,y} \bS_x\cdot\bS_y. The interactions are generally spread-out in the sense that the $J_{x,y}$'s exhibit either exponential or power-law fall-off. Under the technical condition of reflection positivity and for sufficiently spread out interactions, we prove that the model exhibits a first-order phase transition whenever the associated mean-field theory signals such a transition. As a consequence, e.g., in dimensions $d\ge3$, we can finally provide examples of the 3-state Potts model with spread-out, exponentially decaying interactions, which undergoes a first-order phase transition as the temperature varies. Similar transitions are established in dimensions $d=1,2$ for power-law decaying interactions and in high dimensions for next-nearest neighbor couplings. In addition, we also investigate the limit of infinitely spread-out interactions. Specifically, we show that once the mean-field theory is in a unique ``state,'' then in any sequence of translation-invariant Gibbs states various observables converge to their mean-field values and the states themselves converge to a product measure.Comment: 57 pages; uses a (modified) jstatphys class fil

SARS-CoV-2 Omicron-B.1.1.529 leads to widespread escape from neutralizing antibody responses

On 24th November 2021, the sequence of a new SARS-CoV-2 viral isolate Omicron-B.1.1.529 was announced, containing far more mutations in Spike (S) than previously reported variants. Neutralization titers of Omicron by sera from vaccinees and convalescent subjects infected with early pandemic Alpha, Beta, Gamma, or Delta are substantially reduced, or the sera failed to neutralize. Titers against Omicron are boosted by third vaccine doses and are high in both vaccinated individuals and those infected by Delta. Mutations in Omicron knock out or substantially reduce neutralization by most of the large panel of potent monoclonal antibodies and antibodies under commercial development. Omicron S has structural changes from earlier viruses and uses mutations that confer tight binding to ACE2 to unleash evolution driven by immune escape. This leads to a large number of mutations in the ACE2 binding site and rebalances receptor affinity to that of earlier pandemic viruses

The January 2010 Efpalio earthquake sequence in the western Corinth Gulf (Greece)

International audienceThe January 2010 Efpalio earthquake sequence provides some key elements to enhance our view on the western Corinth Gulf tectonics. The sequence lasted almost six months, and included two Mw>5 strong events, both exhibiting normal faulting along approximately E-W trending planes. This paper attempts to construct a unified seismotectonic model of the sequence jointly interpreting earthquake locations, moment-tensors and slip inversions in terms of the possible activated fault planes. Previous studies have connected the prevailing microseismic activity to a major low-angle, north-dipping structure under the Corinth Gulf and the Efpalio sequence favors such a general trend. Moreover, it clearly shows the significance of the shallow activity, so far less recognized, and possibly connected to the relatively steep faults outcropping on the northern coast. The first 18 January 2010 Mw>5 event had almost no on-fault aftershocks and most likely it occurred on a 55 degrees south-dipping nodal plane. The early off-fault aftershocks formed two clusters roughly E-W trending, both of which are connected with normal faulting. Cross-sections revealed that the northernmost cluster is connected with a north-dipping structure, where the second 22 January 2010 Mw>5 event occurred. In addition, the very shallow parts of the faults (<4km) were mainly aseismic, probably due to their creeping behavior. Interestingly, both clusters, at their western and eastern ends, are bounded by NE-SW trending strike-slip faults, a pattern previously observed in normal-faulting structures in Greece. This observation further invokes the role of transfer faults in the western termination of Corinth Gulf, which provide the link with regional structures, such as the Trichonis and Rion-Patras fault systems. Most of all the 2010 Efpalio sequence enhanced the complex mechanical interactions within the Corinth Gulf fault network, with many earthquake generating cluster centers, an observation which has strong implications for the seismic hazard of this densely populated region