H.E. Boos1 Institute for High Energy Physics Protvino, 142284, Russia V.E. Korepin 2 C.N. Yang Institute for Theoretical Physics State University of New York at Stony Brook Stony Brook, NY 11794{3840, USA Abstract Riemann zeta function is an important object of number theory. We argue that it is related to Heisenberg spin 1/2 anti-ferromagnet. In the XXX spin chain we study the probability of f...

Lithium iron orthosilicate (Li2FeSiO4) with Pmn21 space group is theoritically investigated as a chathode material of Li-ion batteries using density functional theory (DFT) calculations. PBE-GGA (+USIC), WC-GGA, L(S)DA (+USIC) and mBJ+LDA(GGA) methods under spin-polarization ferromagnetic (FM) and anti-ferromagnetic (AFM) procedure are used to investigate the material properties, includin...

In this article we apply a recently invented analytical real-space renormalization group formulation which is based on numerical concepts of the density matrix renormalization group. Within a rigorous mathematical framework we construct non-perturbative renormalization group transformations for the spin1 2 XXX Heisenberg model in the finite temperature regime. The developed renormalization grou...

We determine thermal entanglement in mean field clusters of N spin one-half particles interacting via the anisotropic Heisenberg interaction, with and without external magnetic field. For the xxx cluster in the absence of magnetic field we prove that only the N = 2 ferromagnetic cluster shows entanglement. An external magnetic field B can only entangle xxx anti-ferromagnetic clusters in certain...

We address the problem of ”phantom” folding of the tethered membrane modelled by the two-dimensional square lattice, with bonds on the edges and diagonals of each face. Introducing bending rigidities K1 and K2 for respectively long and short bonds, we derive the complete phase diagram of the model, using transfer matrix calculations. The latter displays two transition curves, one corresponding ...

We present theoretical and experimental investigations of the magnetism of paramagnetic semiconductor CdSe:Mn nanocrystals and propose an efficient approach to the exposure and analysis of the underlying anti-ferromagnetic interactions between magnetic ions therein. A key advance made here is the development of an analysis method with the exploitation of group theory technique that allows us to...

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the infinite d-regular tree. More recently S...

Weconsider the Pottsmodelwith q colors on a sequence ofweighted graphs with adjacency matrices An , allowing for both positive and negative weights. Under a mild regularity condition on An we show that the mean-field prediction for the log partition function is asymptotically correct, whenever tr(An) = o(n). In particular, our results are applicable for the Ising and the Potts models on any seq...