Critical Exponents of the Chiral Potts Model from Conformal Field Theory

The $Z_N$-invariant chiral Potts model is considered as a perturbation of a $Z_N$ conformal field theory. In the self-dual case the renormalization group equations become simple, and yield critical exponents and anisotropic scaling which agree with exact results for the super-integrable lattice models. Although the continuum theory is not Lorentz invariant, it respects a novel type of space-time symmetry which allows for the observed spontaneous breaking of translational symmetry in the ground state. The continuum theory is shown to possess an infinite number of conserved charges on the self-dual line, which remain conserved when the theory is perturbed by the energy operator.Comment: 15 page

Onsager's algebra and partially orthogonal polynomials

The energy eigenvalues of the superintegrable chiral Potts model are determined by the zeros of special polynomials which define finite representations of Onsager's algebra. The polynomials determining the low-sector eigenvalues have been given by Baxter in 1988. In the Z_3-case they satisfy 4-term recursion relations and so cannot form orthogonal sequences. However, we show that they are closely related to Jacobi polynomials and satisfy a special "partial orthogonality" with respect to a Jacobi weight function.Comment: 8 pages, no figure

The spreading of SARS-CoV-2: Interage contacts and networks degree distribution

Notable cross-country differences exist in the diffusion of the Covid-19 and in its lethality. Contact patterns in populations, and in particular intergenerational contacts, have been argued to be responsible for the most vulnerable, the elderly, getting infected more often and thus driving up mortality in some context, like in the southern European one. This paper asks a simple question: is it between whom contacts occur that matters or is it simply how many contacts people have? Due to the high number of confounding factors, it is extremely difficult to empirically assess the impact of single network features separately. This is why we rely on a simulation exercise in which we counterfactually manipulate single aspects of countries’ age distribution and network structures. We disentangle the contributions of the kind and of the number of contacts while holding constant the age structure. More precisely, we isolate the respective effects of inter-age contact patterns, degree distribution and clustering on the virus propagation across age groups. We use survey data on face-to-face contacts for Great Britain, Italy, and Germany, to reconstruct networks that mirror empirical contact patterns in these three countries. It turns out that the number of social contacts (degree distribution) largely accounts for the higher infection rates of the elderly in the Italian context, while differences in inter-age contacts patterns are only responsible for minor differences. This suggests that policies specifically targeting inter-age contacts would be little effective

Largely shared neural codes for biological and nonbiological observed movements but not for executed actions in monkey premotor areas

The neural processing of others' observed actions recruits a large network of brain regions (the action observation network; AON) in which frontal motor areas are thought to play a crucial role. As the discovery of mirror neurons (MNs) in the ventral premotor cortex, it has been assumed that their activation was conditional upon the presentation of biological rather than nonbiological motion stimuli, supporting a form of direct visuomotor matching. Nonetheless, nonbiological observed movements have rarely been used as control stimuli to evaluate visual specificity, thereby leaving the issue of similarity among neural codes for executed actions and biological or nonbiological observed movements unresolved. Here, we addressed this issue by recording from two nodes of the AON that are attracting increasing interest, namely, the ventrorostral part of the dorsal premotor area F2 and the mesial presupplementary motor area F6 of macaques while they 1) executed a reaching-grasping task, 2) observed an experimenter performing the task, and 3) observed a nonbiological effector moving in the same context. Our findings revealed stronger neuronal responses to the observation of biological than nonbiological movement, but biological and nonbiological visual stimuli produced highly similar neural dynamics and relied on largely shared neural codes, which in turn remarkably differed from those associated with executed actions. These results indicate that, in highly familiar contexts, visuomotor remapping processes in premotor areas hosting MNs are more complex and flexible than predicted by a direct visuomotor matching hypothesis

Giant entropy change at the co-occurrence of structural and magnetic transitions in the Ni2.19Mn0.81Ga Heusler alloy

In this paper we report the existence of a giant magnetocaloric effect (MCE) in a intermetallic compound non-containing rare-earth. This effect is associated with the concomitant occurrence of a structural and a magnetic transition. The result has been compared with that obtained in a parent compound in which magnetic and structural transition occur separately.Comment: PDF file from MS-Word 2000 document, 13 pages (text) plus 6 figures; corrected typo

Asymmetric XXZ chain at the antiferromagnetic transition: Spectra and partition functions

The Bethe ansatz equation is solved to obtain analytically the leading finite-size correction of the spectra of the asymmetric XXZ chain and the accompanying isotropic 6-vertex model near the antiferromagnetic phase boundary at zero vertical field. The energy gaps scale with size $N$ as $N^{-1/2}$ and its amplitudes are obtained in terms of level-dependent scaling functions. Exactly on the phase boundary, the amplitudes are proportional to a sum of square-root of integers and an anomaly term. By summing over all low-lying levels, the partition functions are obtained explicitly. Similar analysis is performed also at the phase boundary of zero horizontal field in which case the energy gaps scale as $N^{-2}$. The partition functions for this case are found to be that of a nonrelativistic free fermion system. From symmetry of the lattice model under $\pi /2$ rotation, several identities between the partition functions are found. The $N^{-1/2}$ scaling at zero vertical field is interpreted as a feature arising from viewing the Pokrovsky-Talapov transition with the space and time coordinates interchanged.Comment: Minor corrections only. 18 pages in RevTex, 2 PS figure

Nonequilibrium Forces Between Neutral Atoms Mediated by a Quantum Field

We study all known and as yet unknown forces between two neutral atoms, modeled as three dimensional harmonic oscillators, arising from mutual influences mediated by an electromagnetic field but not from their direct interactions. We allow as dynamical variables the center of mass motion of the atom, its internal degrees of freedom and the quantum field treated relativistically. We adopt the method of nonequilibrium quantum field theory which can provide a first principle, systematic and unified description including the intrinsic field fluctuations and induced dipole fluctuations. The inclusion of self-consistent back-actions makes possible a fully dynamical description of these forces valid for general atom motion. In thermal equilibrium we recover the known forces -- London, van der Waals and Casimir-Polder forces -- between neutral atoms in the long-time limit but also discover the existence of two new types of interatomic forces. The first, a `nonequilibrium force', arises when the field and atoms are not in thermal equilibrium, and the second, which we call an `entanglement force', originates from the correlations of the internal degrees of freedom of entangled atoms.Comment: 16 pages, 2 figure

Thermodynamics of the 3-State Potts Spin Chain

We demonstrate the relation of the infrared anomaly of conformal field theory with entropy considerations of finite temperature thermodynamics for the 3-state Potts chain. We compute the free energy and compute the low temperature specific heat for both the ferromagnetic and anti-ferromagnetic spin chains, and find the central charges for both.Comment: 18 pages, LaTex. Preprint # ITP-SB-92-60. References added and first section expande

Matrifocality and child shifting among the low income earners in Jamaica

Jamaican family structures have long felt the impact of unstable internal economic conditions and high volume of labor demands originating from England, Canada, the United States, and other larger societies. In response to the economic conditions and labor demands, increasing numbers of Jamaican women have migrated away from home, both within Jamaica and to other countries. Subsequently, many Jamaicans\u27 households are restructured using a method called child shifting. This refers to the relocation of children between households. Using three major theoretical paradigms: cultural diffusion, social pathology, and structural functionalism, this study explores the literature of child shifting to understand how economic conditions influence matrifocal families and in particular their child rearing practices. This study employs the structural functionalism paradigm\u27s focus on adaptive responses to find plausible explanations for child shifting patterns. The primary premise of the adaptive responses approach is that economic marginality leads to certain adaptive responses in residential, kinship, and child rearing patterns. This study finds certain adjustment problems associated with child shifting. These include shifted children developing feelings of abandonment, of anxiety, of loss, and having difficulty trusting after the shifting occurs. These costs may outweigh the benefits of child shifting