Related papers: Periodic and Weakly Periodic Ground States for the…
We formulate part VI of a rigorous theory of ground states for classical, finite, Heisenberg spin systems. After recapitulating the central results of the parts I - V previously published we consider a magnetic field and analytically…
Two dimensional suspensions of spherical colloids subject to periodic external fields exhibit a rich variety of molecular crystalline phases. We study in simulations the ground state configurations of dimeric and trimeric systems, that are…
In the paper the Ising model with competing $J_1$ and $J_2$ interactions with spin values $\pm 1$, on a Cayley tree of order 2 (with 3 neighbors) is considered . We study the structure of the ground states and verify the Peierls condition…
Ground states and domain walls are investigated with exact combinatorial optimization in two-dimensional random field Ising magnets. The ground states break into domains above a length scale that depends exponentially on the random field…
In this research, methods of reducing a general periodic one-dimensional hopping model to a one- or two-state model, which keeps the basic properties of the original process, are discussed. This reduction also implies that, to some extent,…
Cayley's formula states that the number of labelled trees on $n$ vertices is $n^{n-2}$, and many of the current proofs involve complex structures or rigorous computation. We present a bijective proof of the formula by providing an…
We study the $q$-state clock models on heptagonal lattices assigned on a negatively curved surface. We show that the system exhibits three classes of equilibrium phases; in between ordered and disordered phases, an intermediate phase…
Formation of stationary localized states in one-dimensional chain as well as in a Cayley tree due to a linear impurity and a nonlinear impurity is studied. Furthermore, a one-dimensional chain with linear and nonlinear site energies at the…
Using the 1-loop reduced 3D action of the Abelian Higgs-model we discuss the order of its finite temperature phase transition. A two-variable saddle point approximation is proposed for the evaluation of the effective potential. The strength…
Correlated systems with hexagonal layered structures have come to fore with renewed interest in Cobaltates, transition-metal dichalcogenides and GdI2. While superconductivity, unusual metal and possible exotic states (prevented from long…
We explore the situation where all companion $n \times n$ matrices over a field $F$ are weakly periodic of index of nilpotence $2$ and prove that this can be happen uniquely when $F$ is a countable field of positive characteristic, which is…
In this work, we consider 2D $\mathbb{Z}_2$ topologically ordered phases ($\mathbb{Z}_2$ toric code and the modified surface code) on a simple hyperbolic lattice. Introducing a 2D lattice consisting of the product of a 1D Cayley tree and a…
Let $\omega$ be a factor state on the quasi-local algebra $\cal{A}$ of observables generated by a relativistic quantum field, which in addition satisfies certain regularity conditions (satisfied by ground states and the recently constructed…
We present a general method for determining the phase diagram of systems of a finite number of one dimensional Hubbard--like systems coupled by single--particle hopping with weak interactions. The technique is illustrated by detailed…
In this paper, we continue an investigation of the $p$-adic Ising-Vannimenus model on the Cayley tree of an arbitrary order $k$ $(k\geq 2$). We prove the existence of $p$-adic quasi Gibbs measures by analyzing fixed points of…
A space-periodic ground state is shown to exist for lattices of point ions in $\R^3$ coupled to the Schr\"odinger and scalar fields. The coupling requires the renormalization of the selfaction because of the singularity of the Coulomb…
We show that the Euler walk on a Cayley tree exhibits two regimes (dynamic phases): a condensed phase and a low-density phase. In the condensed phase the self-organized area grows as a compact domain. In the low-density phase the proportion…
We study the Ising model at fixed magnetization on a triangular ladder with three-spin interactions. By recasting the ground-state determination as a linear programming (LP) problem, we solve it exactly using standard LP techniques. We…
The weak nonmesonic decay of Lambda-hypernuclei is studied in the context of a one-meson-exchange model. Predictions are made for the decay rate, p/n stimulation ratio and the asymmetry in polarized hypernuclear decay.
In the present paper, the Ising model with mixed spin-(1,1/2) is considered on the second order Cayley tree. A construction of splitting Gibbs measures corresponding the model is given which allows to establish the existence of the phase…