Related papers: Graphical Representations for Ising Systems in Ext…
The random current representation of the Ising model, along with a related path expansion, has been a source of insight on the stochastic geometric underpinning of the ferromagnetic model's phase structure and critical behavior in different…
The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges of the replica exchange method and the two-replica cluster method and is much more efficient than the…
We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the "cavity" prediction for…
We demonstrate quantum circuit simulations of the transverse field Ising model with longitudinal fields, displaying salient features of glassy dynamics. The energy landscape and spin configurations of toy models are considered, using the…
Reducing a graph while preserving its overall properties is an important problem with many applications. Typically, reduction approaches either remove edges (sparsification) or merge nodes (coarsening) in an unsupervised way with no…
Coupled cluster (CC) has established itself as a powerful theory to study correlated quantum many-body systems. Finite-temperature generalizations of CC theory have attracted considerable interest and have been shown to work as nicely as…
The Ising model on ``thin'' graphs (standard Feynman diagrams) displays several interesting properties. For ferromagnetic couplings there is a mean field phase transition at the corresponding Bethe lattice transition point. For…
In this paper we define a variant of the Ising model in which spins are replaced with permutations. The energy between two spins is a function of the relative disorder of one spin, a permutation, to the other. This model is motivated by a…
A transverse magnetic field is used to scan the diagonal and off-diagonal susceptibility of the uniaxial quantum magnet, $\text{LiHo}_{0.045}\text{Y}_{0.955}\text{F}_4$. Clusters of strongly-coupled spins act as the primary source for the…
In this note, we study the equivalence between planar Ising networks and cells in the positive orthogonal Grassmannian. We present a microscopic construction based on amalgamation, which establishes the correspondence for any planar Ising…
We investigate the Gibbs-measures of ferromagnetically coupled continuous spins in double-well potentials subjected to a random field (our specific example being the $\phi^4$ theory), showing ferromagnetic ordering in $d\geq 3$ dimensions…
It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…
We show that the celebrated six-vertex model of statistical mechanics (along with its multistate generalizations) can be reformulated as an Ising-type model with only a two-spin interaction. Such a reformulation unravels remarkable…
We employ the microcanonical inflection-point analysis method, developed for the systematic identification and classification of phase transitions in systems of any size, to study the two-dimensional Ising model at various lattice sizes and…
The $N$-color Ashkin-Teller model corresponds to $N$ Ising models coupled by four-spin interactions. We consider the two-dimensional case in presence of quenched disorder and use scale invariant scattering theory to determine all the…
We construct a field theory for dissipative systems using a hypercomplex ring formalism that reproduces naturally the effective doubling field formulation of dissipative systems of thermal field theory. The system is quantized by a…
We prove Gibbs distribution of two-state spin systems(also known as binary Markov random fields) without hard constrains on a tree exhibits strong spatial mixing(also known as strong correlation decay), under the assumption that, for…
We study the properties of the double-frequency sine--Gordon model in the vicinity of the Ising quantum phase transition displayed by this model. Using a mapping onto a generalised lattice quantum Ashkin-Teller model, we obtain critical and…
We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…
By combining the beam splitter and the Fresnel transform, a protocol is proposed to generate a new entangled state representation, called the intermediate coherent-entangled state (ICES) representation. The properties, such as eigenvalue…