No Arabic abstract
On this, the occasion of the 20th anniversary of the Ising Lectures in Lviv (Ukraine), we give some personal reflections about the famous model that was suggested by Wilhelm Lenz for ferromagnetism in 1920 and solved in one dimension by his PhD student, Ernst Ising, in 1924. That work of Lenz and Ising marked the start of a scientific direction that, over nearly 100 years, delivered extraordinary successes in explaining collective behaviour in a vast variety of systems, both within and beyond the natural sciences. The broadness of the appeal of the Ising model is reflected in the variety of talks presented at the Ising lectures ( http://www.icmp.lviv.ua/ising/ ) over the past two decades but requires that we restrict this report to a small selection of topics. The paper starts with some personal memoirs of Thomas Ising (Ernsts son). We then discuss the history of the model, exact solutions, experimental realisations, and its extension to other fields.
Motivated by cosmological examples we study quantum field theoretical tunnelling from an initial state where the classical field, i.e. the vacuum expectation value of the field operator is spatially homogeneous but performing a time-dependent oscillation about a local minimum. In particular we estimate both analytically and numerically the exponential contribution to the tunnelling probability. We additionally show that after the tunnelling event, the classical field solution - the so-called bubble - mediating the phase transition can either grow or collapse. We present a simple analytical criterium to distinguish between the two behaviours.
A fresh analysis of Left right symmetric supersymmetric models in the generic case where the scale of right handed symmetry breaking $M_R >> M_{SUSY}sim M_W$ is presented. We conclude that the low energy effective theory for such models is essentially the MSSM with R parity (and therefore B,L symmetry) but the spectrum includes heavy conjugate neutrino supermultiplets that permit a seesaw mechanism and several characteristic charged supermultiplets over and above those of the MSSM.
Recent observations confirm that our universe is flat and consists of a dark energy component $Omega_{DE}simeq 0.7$. This dark energy is responsible for the cosmic acceleration as well as determines the feature of future evolution of the universe. In this paper, we discuss the dark energy of universe in the framework of scalar-tensor cosmology. It is shown that the dark energy is the main part of the energy density of the gravitational scalar field and the future universe will expand as $a(t)sim t^{1.3}$.
We consider a minimal model where the Higgs boson arises as an elementary pseudo-Nambu-Goldstone boson. The model is based on an extended scalar sector with global SO(5)/SO(4) symmetry. To achieve the correct electroweak symmetry breaking pattern, the model is augmented either with an explicit symmetry breaking term or an extra singlet scalar field. We consider separately both of these possibili- ties. We fit the model with the known particle spectrum at the electroweak scale and extrapolate to high energies using renormalization group. We find that the model can remain stable and perturbative up to the Planck scale provided that the heavy beyond Standard Model scalar states have masses in a narrow interval around 3 TeV.
Massive $U(1)$ gauge theories featuring parametrically light vectors are suspected to belong in the Swampland of consistent EFTs that cannot be embedded into a theory of quantum gravity. We study four-dimensional, chiral $U(1)$ gauge theories that appear anomalous over a range of energies up to the scale of anomaly-cancelling massive chiral fermions. We show that such theories require to be UV-completed at a finite cutoff below which a radial mode must appear, and cannot be decoupled -- a Stuckelberg limit does not exist. When the infrared fermion spectrum contains a mixed $U(1)$-gravitational anomaly, this class of theories provides a toy model of a boundary into the Swampland, for sufficiently small values of the vector mass. In this context, we show that the limit of a parametrically light vector comes at the cost of a quantum gravity scale that lies parametrically below $M_{Pl}$, and our result provides field theoretic evidence for the existence of a Swampland of EFTs that is disconnected from the subset of theories compatible with a gravitational UV-completion. Moreover, when the low energy theory also contains a $U(1)^3$ anomaly, the Weak Gravity Conjecture scale makes an appearance in the form of a quantum gravity cutoff for values of the gauge coupling above a certain critical size.