Related papers: Nonexistence and Uniqueness for Pure States of Fer…
We examine the last unexplored regime of the asymmetric six-vertex model: the low-temperature phase of the so-called ferroelectric model. The original publication of the exact solution, by Sutherland, Yang, and Yang, and various derivations…
The notions of pure states and inherent structures, i.e. stable configurations against 1-spin flip are discussed. We explain why these different concepts accidentally coincide in mean-field models with infinite connectivity and present an…
We consider the enumeration of states in the Brubaker-Bump-Friedberg six-vertex model, whose boundary conditions are determined by an integer partition. In general, we find the number of states is a polynomial in the largest part of the…
We study the 6-vertex model with fixed boundary conditions. In the thermodynamical limit there is a formation of the limit shape. We collect most of the known results about the analytical properties of the free energy of the model as the…
We consider a general class of disordered mean-field models where both the spin variables and disorder variables take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate…
The problem of existence and uniqueness of a state of a joint system with given restrictions to subsystems is studied for a Fermion system, where a novel feature is non-commutativity between algebras of subsystems. For an arbitrary (finite…
We consider nonequilibrium systems such as the Edwards-Anderson Ising spin glass at a temperature where, in equilibrium, there are presumed to be (two or many) broken symmetry pure states. Following a deep quench, we argue that as time goes…
We consider a generalised Keller-Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are more singular than Newtonian interaction. We show uniqueness of…
A Hubbard model with a single, partially flat band has ferromagnetic ground states. It is shown that local stability of ferromagnetism implies its global stability in such a model: The model has only ferromagnetic ground states if there are…
A Hubbard model with a N_d-fold degenerate single-particle ground state has ferromagnetic ground states if the number of electrons is less or equal to N_d. It is shown rigorously that the local stability of ferromagnetism in such a model…
We consider a free hydrogen atom composed of a spin-1/2 nucleus and a spin-1/2 electron in the standard model of non-relativistic QED. We study the Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum. For small…
This paper is concerned with the existence of multiple stable fixed point solutions of the homogeneous Kuramoto model. We develop a necessary condition for the existence of stable fixed points for the general network Kuramoto model. This…
The presence of a topological susceptibility in the electroweak sector of the Standard Model implies the existence of a pseudoscalar state in the spectrum, $\eta_W$. We show that, within the Standard Model, no new particle is required to…
We consider a huge quantum system that is subject to the charge superselection rule, which requires that any pure state must be an eigenstate of the total charge. We regard some parts of the system as "subsystems," and the rest as an…
We analyze the equilibrium states of quantum lattice model with local multi-well potentials for Sn$_2$P$_2$S$_6$ ferroelectric crystals using the mean and Gaussian curvatures ($H$, $K$), curvedness ($C$) and shape index ($S$). From the…
We study the tight-binding model with two distinct hoppings $(t_L, t_S)$ on the two-dimensional hexagonal golden-mean tiling and examine the confined states with $E=0$, where $E$ is the eigenenergy. Some confined states found in the case…
We study the free energy landscape of a minimal model for relaxor ferroelectrics. Using a variational method which includes leading correlations beyond the mean-field approximation as well as disorder averaging at the level of a simple…
The Nelson model, describing a quantum mechanical particle linearly coupled to a bosonic field, exhibits the infrared problem in the sense that no ground state exists at arbitrary total momentum. However, passing to a non-Fock…
We discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same…
It is well known that the Hubbard model on a line graph has a flat band and ferromagnetic ground states in a certain density range. We show that for a Hubbard model on a line graph of a planar bipartite graph the ferromagnetic ground state…