A Lorentzian inversion formula for defect CFT

We present a Lorentzian inversion formula valid for any defect CFT that extracts the bulk channel CFT data as an analytic function of the spin variable. This result complements the already obtained inversion formula for the corresponding defect channel, and makes it now possible to implement the analytic bootstrap program for defect CFT, by going back and forth between bulk and defect expansions. A crucial role in our derivation is played by the Calogero-Sutherland description of defect blocks which we review. As first applications we obtain the large-spin limit of bulk CFT data necessary to reproduce the defect identity, and also calculate one-point functions of the twist defect of the 3d Ising model to first order in the ϵ-expansion.

Spin variable approach for the statistical mechanics of folding and unfolding chains

Force–extension relations for stretching experiments under isotensional and isometric conditions are obtained through the spin variable approach.

MODELING DARK ENERGY THROUGH AN ISING FLUID WITH NETWORK INTERACTIONS

We show that the dark energy (DE) effects can be modeled by using an Ising perfect fluid with network interactions, whose low redshift equation of state (EoS), i.e. ω0, becomes ω0 = -1 as in the ΛCDM model. In our picture, DE is characterized by a barotropic fluid on a lattice in the equilibrium configuration. Thus, mimicking the spin interaction by replacing the spin variable with an occupational number, the pressure naturally becomes negative. We find that the corresponding EoS mimics the effects of a variable DE term, whose limiting case reduces to the cosmological constant Λ. This permits us to avoid the introduction of a vacuum energy as DE source by hand, alleviating the coincidence and fine tuning problems. We find fairly good cosmological constraints, by performing three tests with supernovae Ia (SNeIa), baryonic acoustic oscillation (BAO) and cosmic microwave background (CMB) measurements. Finally, we perform the Akaike information criterion (AIC) and Bayesian information criterion (BIC) selection criteria, showing that our model is statistically favored with respect to the Chevallier–Polarsky–Linder (CPL) parametrization.

CRITICAL TEMPERATURES OF THE ISING MODEL ON THE BETHE LATTICE FOR ARBITRARY VALUES OF SPIN

Using the method of recursion relations an exact solution of classical Ising models with arbitrary value of spin on the Bethe lattice with arbitrary coordination number is presented. Expressions for the spontaneous magnetization, for the magnetic moments of arbitrary orders, for the susceptibility, for the free energy, and for the specific heat are found as functions of quantities which are determined by the recursion relations. The behavior of the spontaneous magnetization for the Ising model on the Bethe lattice is investigated for systems with spin values up to s = 5 for various coordination numbers and the corresponding critical temperatures are determined. An approximate formula for determining the positions of the critical temperatures for arbitrary high values of the spin variable is found and discussed. It is shown that this formula allows one to determine the full structure of the critical temperatures with very high precision.

CHAOTIC MODES IN SCALE FREE OPINION NETWORKS

In this paper, we investigate processes associated with formation of public opinion in varies directed random, scale free and small-world social networks. The important factor of the opinion formation is the existence of contrarians which were discovered by Granovetter in various social psychology experiments1,2,3 long ago and later introduced in sociophysics by Galam.4 When the density of contrarians increases the system behavior drastically changes at some critical value. At high density of contrarians the system can never arrive to a consensus state and periodically oscillates with different periods depending on specific structure of the network. At small density of the contrarians the behavior is manifold. It depends primary on the initial state of the system. If initially the majority of the population agrees with each other a state of stable majority may be easily reached. However when originally the population is divided in nearly equal parts consensus can never be reached. We model the emergence of collective decision making by considering N interacting agents, whose opinions are described by two state Ising spin variable associated with YES and NO. We show that the dynamical behaviors are very sensitive not only to the density of the contrarians but also to the network topology. We find that a phase of social chaos may arise in various dynamical processes of opinion formation in many realistic models. We compare the prediction of the theory with data describing the dynamics of the average opinion of the USA population collected on a day-by-day basis by varies media sources during the last six month before the final Obama-McCain election. The qualitative ouctome is in reasonable agreement with the prediction of our theory. In fact, the analyses of these data made within the paradigm of our theory indicates that even in this campaign there were chaotic elements where the public opinion migrated in an unpredictable chaotic way. The existence of such a phase of social chaos reflects a main feature of the human being associated with some doubts and uncertainty and especially associated with contrarians which undoubtly exist in any society.

MAGNETIC PAIRING IN TWO-DIMENSIONAL ANTIFERROMAGNETIC XY MODEL

A two-dimensional Ising Coulomb gas is introduced to describe the frustrated plaquettes of the two-dimensional antiferromagnetic XY model with Coulomb repulsion. The Ising spin variable corresponds to the two possible chiralities of the frustrated plaquettes, which repel each other with a screened Coulomb potential. Using the self-consistent screening analysis, the Ising Coulomb gas is shown to have a Kosterlitz-Thouless transition from a pairing phase at low temperature to a plasma phase at high temperature. The phase diagram is obtained numerically as a function of density and relative strength of the attraction between particles of opposite chiralities and the Coulomb repulsion. Possible applications to the magnetic pairing mechanism of high temperature superconductors is discussed in the context of Li doped La 2 CuO 4. It is also argued that the Aharony et al. model of magnetic pairing with the dipolar attraction can be derived as a special case of the Ising Coulomb gas model and is superceded by a stronger attractive interaction in magnetic pairing mechanism in the self-consistent analysis.