Related papers: Hard-Core and Soft-Core Widom-Rowlinson models on …
In the paper, we consider the $\lambda$-model with spin values $\{1, 2, 3\}$ on the Cayley tree of order two. We first describe ground states of the model. Moreover, we also proved the existence of translation-invariant Gibb measures for…
We consider a coupled Ising-Potts model on Cayley trees of order $ k \geq 2 $. This model involves spin vectors $ (s, \sigma) $, and generalizes both the Ising and Potts models by incorporating interactions between two types of spins: $s =…
In this paper, we consider Vannimenus model with competing nearest-neighbors and prolonged next-nearest-neighbors interactions on a Cayley tree. For this model we define Markov random fields with memory of length 2. By using a new approach,…
The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics. We show that for both the hard-core (independent set) model and the anti-ferromagnetic Ising…
In this paper, we investigate multi-soft behaviors of tree amplitudes in nonlinear sigma model (NLSM). The leading behaviors of amplitudes with odd number of all-adjacent soft pions are zero. We further propose and prove that leading soft…
We analyze the spectrum and properties of a highly-deconstructed Higgsless model with only three sites. Such a model contains sufficient complexity to incorporate interesting physics issues related to fermion masses and electroweak…
In this present paper, the recurrence equations of an Ising model with three coupling constants on a third-order Cayley tree are obtained. Paramagnetic and ferromagnetic phases associated with the Ising model are characterized. Types of…
We consider translation-invariant splitting Gibbs measures (TISGMs) for the $q$-state Potts model on a Cayley tree of order two. Recently a full description of the TISGMs was obtained, and it was shown in particular that at sufficiently low…
In this paper we construct several models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 2$. We prove that each of the constructed model has at least two translational-invariant…
The phase transition phenomenon is one of the central problems of statistical mechanics. It occurs when the model possesses multiple Gibbs measures. In this paper, we consider a three-state SOS (solid-on-solid) model on a Cayley tree. We…
For the solid-on-solid (SOS) model with spin values from the set of all integers on a Cayley tree we give gradient Gibbs measures (GGMs). Such a measure corresponds to a boundary law (which is an infinite-dimensional vector-valued function…
To understand the role of local sublattice imbalance in low-energy spectra of s=1/2 quantum antiferromagnets, we study the s=1/2 quantum nearest neighbor Heisenberg antiferromagnet on the coordination 3 Cayley tree. We perform many-body…
In the present paper, we study the $(2,q)$-Ising-Potts model on the Cayley tree. We have derived a recurrence equation that shows the existence of a splitting Gibbs measure for this model. Furthermore, we have proven that for the…
In this paper we consider a model with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k \geq 2$. To study translation-invariant Gibbs measures of the model we drive an nonlinear functional…
We use a combination of a many-body model analysis with an ab initio band structure calculation to derive the temperature dependent electronic quasiparticle structure of the rare-earth metal Gadolinium. As a local-moment system Gd is…
We consider the Widom--Rowlinson model in which hard balls of two possible colors are constrained to a hard-core repulsion between particles of different colors, in quenched random environments. These random environments model spatially…
We study the hard-core model defined on independent sets, where each independent set I in a graph G is weighted proportionally to $\lambda^{|I|}$, for a positive real parameter $\lambda$. For large $\lambda$, computing the partition…
Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model…
We investigate the location of zeros for the partition function of the anti-ferromagnetic Ising Model, focusing on the zeros lying on the unit circle. We give a precise characterization for the class of rooted Cayley trees, showing that the…
In this paper, we extend the method proposed in \cite{Arkani-Hamed:2024fyd} for deriving soft theorems of amplitudes, which relies exclusively on factorization properties including conventional factorizations on physical poles, as well as…