We discuss three exactly solvable spin models of geometric frustration. First, we a 1-parameter subfamily the 16 vertex model, which can be mapped to planar Ising model and solved via Fisher-Dubedát decorations. then consider family generalization Villain’s fully frustrated interpolates between Onsager’s 2D Villain one. ice on tree, using recursions lá Bethe.

environmental pollution with heavy metals is a global struggle. phytoremediation is an effectiveand low-cost technology for refinement of polluted soils. this research was conducted in zanjan province(located in north west iran) where metallurgical industries are developed quickly. in this study, based on theheavy metals contamination of soil in the studied area six sampling sites were selected...

The recently established generalized Gell-Mann–Low theorem is applied in lowest perturbative order to bound–state calculations in a simple scalar field theory with cubic couplings. The approach via the generalized Gell-Mann–Low Theorem retains, while being fully relativistic, many of the desirable features of the quantum mechanical approaches to bound states. In particular, no abnormal or unphy...

We investigate different ways of generating approximate solutions to the pairwise Markov random field (MRF) selection problem. We focus mainly on the inverse Ising problem, but discuss also the somewhat related inverse Gaussian problem because both types of MRF are suitable for inference tasks with the belief propagation algorithm (BP) under certain conditions. Our approach consists in to take ...

Many practical hard problems in mathematics and computer science may be formulated as constraint satisfaction problems (CSPs). Tree and generalized hypertree decompositions are two important concepts which can be used for identifying and solving tractable classes of CSPs. Unfortunately the task of finding an optimal tree or generalized hypertree decomposition is an NP-complete problem. Thus man...

A simple method, previously used to calculate the equilibrium concentration of dimers adsorbed on a Bethe lattice as a function of the dimer activity, is generalized to solve the problem of a Bethe lattice in contact with a reservoir containing a mixture of molecules. The molecules may have arbitrary sizes and shapes consistent with the geometry of the lattice and the molecules do not interact ...

The Global Color-symmetry Model of QCD is extended to deal with a background electromagnetic field and the associated conserved current is identified for composite ¯ qq pion modes of the model. Although the analysis is limited to tree level in the bilocal fields that bosonize the model, the identified photon-pion vertex produces the charge form factor associated with ladder Bethe-Salpeter pion ...

The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional approach, where the BSE is solved in Euclidean space after a Wick rotation. For all but the lowest-order (i.e., ladder) approximation to the scattering kernel, the naive Wick rotation is...