We consider a mean-field continuum model of classical particles in Rd with Ising or Heisenberg spins. The interaction has two ingredients, a ferromagnetic spin coupling and a spin-independent molecular force. We show that a feedback between these forces gives rise to a first-order phase transition with simultaneous jumps of particle density and magnetization per particle, either at the threshol...

It is shown that the continuum limit of the spin 1/2 Heisenberg XYZ model is far from sufficient for the site number of 16. Therefore, the energy spectrum of the XYZ model obtained by Kolanovic et al. has nothing to do with the massive Thirring model, but it shows only the spectrum of the finite size effects. The spin 1/2 Heisenberg model is a rich theory, which contains a variety of field theo...

Heisenberg, in constructing quantum mechanics, explicitly followed certain principles exemplified, as he believed, in Einstein's construction of the special theory of relativity which for him was the paradigm for radical theoretic change in physics. These were the principles of (i) scientific realism, (ii) stability of background knowledge, (iii) E-observability, (iv) contextual re-interpretati...

We study the strong coupling limit of the 2-flavor massless Schwinger model on a lattice using staggered fermions and the Hamiltonian approach to lattice gauge theories. Using the correspondence between the low-lying states of the 2-flavor strongly coupled lattice Schwinger model and the antiferromagnetic Heisenberg chain established in a previous paper, we explicitly compute the mass spectrum ...

Using exact diagonalization techniques, we study the dynamical response of the anisotropic disordered Heisenberg model for systems of S=1/2 spins with infinite range random exchange interactions at temperature T=0. The model can be considered as a generalization, to the quantum case, of the well-known Sherrington-Kirkpatrick classical spin glass model. We also compute and study the behavior of ...

We obtain the variational upper bound for the groundstate energy of twodimensional antiferromagnetic Heisenberg model on a square lattice at arbitrary value of the anisotropy parameter using the two-dimensional generalization of Jordan-Wigner transformation. Our result can be considered as an upper bound for the perturbation theory series about the Ising limit. At present time two dimensional q...

We study a simplified Heisenberg spin model in order to clarify the idea of decoherence in closed quantum systems. For this purpose, we define a new concept: the coherence function Ξ(t), which describes the dynamics of coherence in the whole system, and which is linked with the total coarsegrained (von Neumann) entropy of all particles. We discuss in some detail a general coherence theory and i...

Ground-state energies for plaquette and dimer order in the J1-J2 square-lattice spin-half Heisenberg model are compared using series expansion methods. We find that these energies are remarkably close to each other at intermediate values of J2 /J1 , where the model is believed to have a quantum disordered ground state. They join smoothly with those obtained from the Ising expansions for the two...

We study two planar square lattice Heisenberg models with explicit dimerization or quadrumerization of the couplings in the form of ladder and plaquette arrangements. We investigate the quantum critical points of those models by means of stochastic series expansion quantum Monte Carlo simulations as a function of the coupling ratio =J /J. The critical point of the order-disorder quantum phase t...

Spin-1/2 Ising-Heisenberg model with XY Z Heisenberg pair interaction and two different Ising quartic interactions is exactly solved with the help of the generalized star-square transformation, which establishes a precise mapping equivalence with the corresponding eight-vertex model on a square lattice generally satisfying Baxter’s zero-field (symmetric) condition. The investigated model exhibi...