Exact Expressions for Minor Hysteresis Loops in the Random Field Ising Model on a Bethe Lattice at Zero Temperature

We obtain exact expressions for the minor hysteresis loops in the ferromagnetic random field Ising model on a Bethe lattice at zero temperature in the case when the driving field is cycled infinitely slowly.Comment: Replaced with the published versio

Electron Correlations and Two-Photon States in Polycyclic Aromatic Hydrocarbon Molecules: A Peculiar Role of Geometry

We present numerical studies of one- and two-photon excited states ordering in a number of polycyclic aromatic hydrocarbon molecules: coronene, hexa-peri-hexabenzocoronene and circumcoronene, all possessing $D_{6h}$ point group symmetry versus ovalene with $D_{2h}$ symmetry, within the Pariser-Parr-Pople model of interacting $\pi$-electrons. The calculated energies of the two-photon states as well as their relative two-photon absorption cross-sections within the interacting model are qualitatively different from single-particle descriptions. More remarkably, a peculiar role of molecular geometry is found. The consequence of electron correlations is far stronger for ovalene, where the lowest spin-singlet two-photon state is a quantum superposition of pairs of lowest spin triplet states, as in the linear polyenes. The same is not true for $D_{6h}$ group hydrocarbons. Our work indicates significant covalent character, in valence bond language, of the ground state, the lowest spin triplet state and a few of the lowest two-photon states in $D_{2h}$ ovalene but not in those with $D_{6h}$ symmetry.Comment: 11 pages, 3 figures, 3 table

Augmented Superfield Approach to Nilpotent Symmetries in the Modified Version of 2D Proca Theory

We derive the complete set of off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations for all the fields of the modified version of two (1+1)-dimensional (2D) Proca theory by exploiting the "augmented" superfield formalism where the (dual-)horizontality conditions and (dual-)gauge-invariant restrictions are exploited together. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian density in the language of superfield formalism. We also express the nilpotency and absolute anticommutativity of the (anti-)BRST and (anti-)co-BRST charges within the framework of augmented superfield formalism. This exercise leads to some novel observations which have, hitherto, not been pointed out in the literature within the framework of superfield approach to BRST formalism. For the sake of completeness, we also mention, very briefly, a unique bosonic symmetry, the ghost-scale symmetry and discrete symmetries of the theory and show that the algebra of conserved charges captures the cohomological aspects of differential geometry. Thus, our present modified 2D Proca theory is a model for the Hodge Theory.Comment: LaTeX file, 32 pages, journal reference give