We prove that Nelson’s massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian has no ground state in Fock space and thus it is not unitarily equivalent with the Hamiltonian obtained from Euclidean quantization. In contrast, for dimensions higher than three the Nelson Hamiltonian has a unique ground state in Fock space and the two Hamiltonian...

If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.

If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.

If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.

We derive the nested Bethe Ansatz solution of the fully packed O(n) loop model on the honeycomb lattice. From this solution we derive the bulk free energy per site along with the central charge and geometric scaling dimensions describing the critical behaviour. In the n = 0 limit we obtain the exact compact exponents γ = 1 and ν = 1/2 for Hamiltonian walks, along with the exact value κ2 = 3 √ 3...

Consider Ising spins Sn = ±1interacting under a i3R(2~m)>ln(1 +~,fi) = 0.88137..., hamiltonian H — ~ J~~ with >0 let < denote expectations in this model at inverse temperato be compared with the mean field value 0.5 (which ture 13. Let ç = (c~),a~2))= (cos°a’sin On) be twowas known [21* 1 to be a lower bound on 13~), the component uniformly distributed unit vectors and let gaussian value 2/ir =...

In this paper, a symplectic model reduction technique, proper symplectic decomposition (PSD) with symplectic Galerkin projection, is proposed to save the computational cost for the simplification of large-scale Hamiltonian systems while preserving the symplectic structure. As an analogy to the classical proper orthogonal decomposition (POD)-Galerkin approach, PSD is designed to build a symplect...

An effective action in Hamiltonian form is derived for a self-gravitating sphere of isotropic homogeneous dust. Starting from the Einstein-Hilbert action for barotropic perfect fluids and making use of the symmetry and equation of state of the matter distribution we obtain a family of reduced actions for two canonical variables, namely the radius of the sphere and its ADM energy, the latter bei...

We show that the recently constructed exact solution of the SU(2|2) extended Hub-bard model on a one-dimensional lattice provides a complete set of 4 L eigenstates of the hamiltonian, where L is the length of the lattice.