Fermionic observables in the transverse Ising chain

We introduce a notion of s-holomorphicity suitable for certain quantum spin systems in one dimension, and define two observables in the critical transverse-field Ising model which have this property. The observables are defined using graphical representations in the complex plane, and are analogous to Smirnov's FK-Ising and spin-Ising observables, respectively. We also briefly discuss scaling-limits of these observables.Comment: 32 page

Large cycles in random permutations related to the Heisenberg model

We study the weighted version of the interchange process where a permutation receives weight $\theta^{\#\mathrm{cycles}}$. For $\theta=2$ this is T\'oth's representation of the quantum Heisenberg ferromagnet on the complete graph. We prove, for $\theta>1$, that large cycles appear at `low temperature'.Comment: 11 page

Critical temperature of Heisenberg models on regular trees, via random loops

We estimate the critical temperature of a family of quantum spin systems on regular trees of large degree. The systems include the spin-$\frac12$ XXZ model and the spin-1 nematic model. Our formula is conjectured to be valid for large-dimensional cubic lattices. Our method of proof uses a probabilistic representation in terms of random loops.Comment: 14 pages, to appear in J. Stat. Phy

The Anharmonic Correction in the Soliton Model for the Hyperons

We derive the anharmonic correction to the hyperon energy in the bound state version of the topological soliton model for the hyperons, and show that it represents a negative correction of at most 10% to the energy of the bound heavy flavour two-meson system in the case of cascade hyperons. The main anharmonic correction arises from the mass term in the Lagrangian density. For large meson masses the consistency of the model requires that the anharmonic correction decreases as the inverse square root of the mass of the heavy flavour meson.Comment: 19 page

Uusiutuva energiajärjestelmä Suomessa –uuden teknologian investoinnin anaysointi terästeollisuudessa

The comparison of four future renewable energy system scenarios yields that energy system design for futures with 100% renewable energy is greatly dependent on whether the objective is to design an energy system with 100% renewable energy or to reduce GHG emissions from society as a whole. The latter seems to increase the relevance of power-to-gas (PtG) and power-to-liquid (PtL) technologies as these have the capacity to abate emissions from some industrial processes. Common fac-tors in the four scenarios compared are higher electrification of the energy system and deeper integration of the enery sectors transport, heating and electricity. Differences between scenarios include biomass availability assumptions, level of electrification of transport, the inclusion of CCS, and the role of PtG/PtL as well as the level of integration of non-energy sectors with the energy system. A main finding is that biomass availability assumptions vary greatly illustrating the uncertainty connected to future energy system research, and that these also seem to affect the role of PtG/PtL technologies. In addition, the drivers for investment in PtG/PtL differ between countries, with the technology playing a larger role in balancing inter-mittent renewable electricity sources in the scenario that relies very little on bioenergy. Furthermore, the transport and industry sectors are found to be the two hardest sectors to decarbonise. A business case related to the integration of PtL technology in an existing steel mill in Raahe, Finland is studied with the decision supporting Robust Decision Making (RDM) method. Results indicate that other investment options are more robust to future uncertainties than the PtL option is, but that RDM can be a useful tool when evaluating decisions made under conditions of deep uncertainty. RDM can offer a deeper understanding of the risks in far-reaching decisions and offer new perspec-tives in energy system analysis. Simultanoeusly, it also requires more time and commitment than a normal cost-benefit analysis.Neljän EU-maiden tutkimuslaitosten laatimat tulevaisuusskenaariot 100% uusiutuvista energiajärjestelmistä verrataan keskenään ja yhteistä kaikille on lisääntynyt sähköistäminen sekä sähko- lämpö ja liikennesektoreiden kytkentä. Skenaarioiden tavoitteet vaihtelevat 100% uusiutuvan energiajärjestelmän suunnittelusta aina kasvihuonepäästöneutraalin yhteiskunnan suunnitteluun, ja skenaarion tavoitteella havaittiin olevan vaikutus energiajärjestelmän suunnitteluun. Skenaarioien välillä on suuria eroja biomassan saatavuuden oletuksissa, oletuksissa CCS:än käytöstä sekä synteettisesti tuotettujen energiaintensiivisten kaasujen ja nesteiden (PtG, PtL) tärkeydessä ja roolissa. Myös ei-energiasektoreiden kytkentä energiasektoreihin vaihtelee skenaarioiden välillä. Keskeisiä tuloksia ovat teolli-suussektorin päästövähennystavoitteiden sekä biomassan saatavuudesta tehtyjen oletusten vaikutus PtG/PtL teknologioiden tärkeyteen osana energiajärjestelmää. Tämän lisäksi se, että teollisuus ja liikenne ovat kaikista vaikeampia sektoreita päästöjen vähentämiseen on myös vertauksen tulos. Skenaarioiden vertailusta käy ilmi, että tulevaisuuden energiajärjestelmien suunnitteluskenaarioihin sisältyy merkittävä määrä epävarmuutta; aina teknisistä ratkaisuista sosiaalisiin, poliittisiin ja taloudellisiin kysymyksiin. Suomailaiseen terästeollisuuteen ja PtL teknologiaan kytkeytyvä investointipäätös analysoidaan Robust Decision Making (RDM) –menetelmällä, jota on suunniteltu isojen epävarmuuksien alla tehtyjen päätösten tueksi. Tulokset osoittavat, että PtL –investointi ei ole yhtä robusti vaihtoehto kuin monet muut investointivaihtoehdot, mutta että RDM –menetelmän sovelluksesta vastaavanlaisiin tapauksiin voi olla hyötyä. RDM voi antaa syvemmän ymmärryksen riskeistä, mutta sen käyttäminen vaatii enemmän aikaa ja sitoutumista kuin perinteinen teknillis-taloudellinen mallintaminen

The occurrence of Amphioxides pelagicus (Günther) in the Fernando de Noronha Island plankton

Trata o presente trabalho do encontro de duas larvas de Acrania, no plancton da Ilha Fernando de Noronha. Esse material, frequentemente considerado como larva de Asymmetron lucayanum, foi determinado por Vannucci como sendo de Amphioxides pelagicus (Günther). Os adultos e as larvas dos Acrania tem hábitos de vida um pouco diferentes. Por isso as larvas desse tipo foram sempre objeto de controvérsias. Pensou-se de início, que se tratava de formas adultas adaptadas a vida pelágica mas, atualmente, são consideradas como estádios larvares de adultos de anfioxo, a vista de exibirem vários caracteres peculiares as larvas desse animal. Concluindo, o autor explica como esta forma pode ser considerada como ama espécie definitivamente separada, produzida por seus hábitos peculiares de reprodução e por sua ecologia, desde que seja provado tratar-se de uma pedomorfose estabelecida

Graphical representations of Ising and Potts models: stochastic geometry of the quantum Ising model and the space-time Potts model

Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. These models in turn are part of the unifying framework of the random-cluster representation, a model for random graphs which was first studied by Fortuin and Kasteleyn in the 1970’s. The random-cluster representation has proved extremely useful in proving important facts about the Ising model and similar models. In this work we study the corresponding graphical framework for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960’s. The second model is the space–time percolation process, which is closely related to the contact model for the spread of disease. In Chapter 2 we define the appropriate ‘space–time’ random-cluster model and explore a range of useful probabilistic techniques for studying it. The space–time Potts model emerges as a natural generalization of the quantum Ising model. The basic properties of the phase transitions in these models are treated in this chapter, such as the fact that there is at most one unbounded fk-cluster, and the resulting lower bound on the critical value in Z. In Chapter 3 we develop an alternative graphical representation of the quantum Ising model, called the random-parity representation. This representation is based on the random-current representation of the classical Ising model, and allows us to study in much greater detail the phase transition and critical behaviour. A major aim of this chapter is to prove sharpness of the phase transition in the quantum Ising model—a central issue in the theory—and to establish bounds on some critical exponents. We address these issues by using the random-parity representation to establish certain differential inequalities, integration of which give the results. In Chapter 4 we explore some consequences and possible extensions of the results established in Chapters 2 and 3. For example, we determine the critical point for the quantum Ising model in Z and in ‘star-like’ geometries