Complete characterization of spin chains with two Ising symmetries

Spin chains with two Ising symmetries are the Jordan-Wigner duals of one-dimensional interacting fermions with particle-hole and time-reversal symmetry. From earlier works on Majorana chains, it is known that this class of models has 10 distinct topological phases. In this paper, we analyze the physical properties of the correspondent 10 phases of the spin model. In particular, thanks to a set of two non-commuting dualities, we determine the local and non-local order parameters of the phases. We find that 4 phases are topologically protected by the Ising symmetries, while the other 6 break at least one symmetry. Our study highlights the non-trivial relation between the topological classifications of interacting bosons and fermions.Comment: 7 page

Fingerprinting Hysteresis

We test the predictive power of first-oder reversal curve (FORC) diagrams using simulations of random magnets. In particular, we compute a histogram of the switching fields of the underlying microscopic switching units along the major hysteresis loop, and compare to the corresponding FORC diagram. We find qualitative agreement between the switching-field histogram and the FORC diagram, yet differences are noticeable. We discuss possible sources for these differences and present results for frustrated systems where the discrepancies are more pronounced.Comment: 4 pages, 5 figure

Fossil evidence for a pharyngeal origin of the vertebrate pectoral girdle

The origin of vertebrate paired appendages is one of the most investigated and debated examples of evolutionary novelty. Paired appendages are widely considered key innovations that allowed new opportunities for controlled swimming and gill ventilation and were prerequisites for the eventual transition from water to land. The last 150 years of debate has been shaped by two contentious theories: the ventrolateral fin-fold hypothesis and the archipterygium hypothesis. The latter proposes that fins and girdles evolved from an ancestral gill arch. Although tantalizing developmental evidence has revived interest in this idea, it is apparently unsupported by fossil evidence. Here we present fossil evidence of a pharyngeal basis for the vertebrate shoulder girdle. We use CT scanning to reveal details of the braincase of Kolymaspis sibirica, a placoderm fish from the Early Devonian of Siberia that suggests a pharyngeal component of the shoulder. We combine these findings with refreshed comparative anatomy of placoderms and jawless outgroups to place the origin of the shoulder girdle on the sixth branchial arch. These findings provide a novel framework for understanding the origin of the pectoral girdle. Our new evidence clarifies the location of the presumptive head-trunk interface in jawless fishes and explains the constraint on branchial arch number in gnathostomes. The results revive a key aspect of the archipterygium hypothesis, but also reconciles it with the ventrolateral fin fold model

On backward stochastic differential equations and strict local martingales

We study a backward stochastic differential equation whose terminal condition is an integrable function of a local martingale and generator has bounded growth in $z$. When the local martingale is a strict local martingale, the BSDE admits at least two different solutions. Other than a solution whose first component is of class D, there exists another solution whose first component is not of class D and strictly dominates the class D solution. Both solutions are $\mathbb{L}^p$ integrable for any $0<p<1$. These two different BSDE solutions generate different viscosity solutions to the associated quasi-linear partial differential equation. On the contrary, when a Lyapunov function exists, the local martingale is a martingale and the quasi-linear equation admits a unique viscosity solution of at most linear growth.Comment: Keywords: Backward stochastic differential equation, strict local martingale, viscosity solution, comparison theore

Non-monotonic field-dependence of the ZFC magnetization peak in some systems of magnetic nanoparticles

We have performed magnetic measurements on a diluted system of gamma-Fe2O3 nanoparticles (~7nm), and on a ferritin sample. In both cases, the ZFC-peak presents a non-monotonic field dependence, as has already been reported in some experiments,and discussed as a possible evidence of resonant tunneling. Within simple assumptions, we derive expressions for the magnetization obtained in the usual ZFC, FC, TRM procedures. We point out that the ZFC-peak position is extremely sensitive to the width of the particle size distribution, and give some numerical estimates of this effect. We propose to combine the FC magnetization with a modified TRM measurement, a procedure which allows a more direct access to the barrier distribution in a field. The typical barrier values which are obtained with this method show a monotonic decrease for increasing fields, as expected from the simple effect of anisotropy barrier lowering, in contrast with the ZFC results. From our measurements on gamma-Fe2O3 particles, we show that the width of the effective barrier distribution is slightly increasing with the field, an effect which is sufficient for causing the observed initial increase of the ZFC-peak temperatures.Comment: LaTeX file 19 pages, 9 postscript figures. To appear in Phys. Rev. B (tentative schedule: Dec.97