Related papers: The planar Ising model and total positivity

We investigate the zero-temperature quantum phase transition of the random bond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two…

We present an exact analytical solution for the one-dimensional Ising model in the presence of an external magnetic field applied periodically to every $k$-th site. The problem is handled using the symmetrized transfer matrix approach, we…

The partition function of the Ising model of a graph $G=(V,E)$ is defined as $Z_{\text{Ising}}(G;b)=\sum_{\sigma:V\to \{0,1\}} b^{m(\sigma)}$, where $m(\sigma)$ denotes the number of edges $e=\{u,v\}$ such that $\sigma(u)=\sigma(v)$. We…

A linear map between real symmetric matrix spaces is positive if all positive semidefinite matrices are mapped to positive semidefinite ones. A real symmetric matrix is separable if it can be written as a summation of Kronecker products of…

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the…

We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the…

We study the three-dimensional quantum Ising spin glass in a transverse magnetic field following the evolution of the bond probability distribution under Renormalisation Group transformations. The phase diagram (critical temperature $T_c$…

The process of alternately row scaling and column scaling a positive $n \times n$ matrix $A$ converges to a doubly stochastic positive $n \times n$ matrix $S(A)$, often called the \emph{Sinkhorn limit} of $A$. The main result in this paper…

We consider a class of non-integrable 2D Ising models, whose Hamiltonian, in addition to the nearest neighbor couplings, includes weak multi-spin interactions, even under spin flip. We study the model in cylindrical domains of arbitrary…

Let $V$ be a nonempty finite set and $A=(a_{ij})_{i,j\in V}$ be a matrix with entries in a field $\mathbb{K}$. For a subset $X$ of $V$, we denote by $A[X]$ the submatrix of $A$ having row and column indices in $X$. We study the following…

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…

We consider the Ising model on a $d$-dimensional discrete torus of volume $r^d$, in dimensions $d>4$ and for large $r$, in the vicinity of the infinite-volume critical point $\beta_c$. We prove that for $\beta=\beta_c- {\rm const}\,…

We pose the deterministic, nonparametric, approximation problem for scalar nonnegative input/output systems via finite impulse response convolutions, based on repeated observations of input/output signal pairs. The problem is converted into…

The one-dimensional transverse Ising model is a paradigmatic example of quantum criticality. In spin-orbit coupled systems, however, effective Ising interactions arise alongside bond-dependent couplings such as Kitaev ($K$) and $\Gamma$…

We investigate, by means of extensive Monte Carlo simulations, the magnetic critical behavior of the three-dimensional bimodal random-field Ising model at the strong disorder regime. We present results in favor of the two-exponent scaling…

We study the scaling of the traces of the integer powers of the partially transposed reduced density matrix and of the entanglement negativity for two spin blocks as function of their length and separation in the critical Ising chain. For…

Positive maps which are not completely positive are used in quantum information theory as witnesses for convex sets of states, in particular as entanglement witnesses and more generally as witnesses for states having Schmidt number not…

Transfer-matrix methods are used to calculate spin-spin correlation functions ($G$), Helmholtz free energies ($f$) and magnetizations ($m$) in the two-dimensional random-field Ising model close to the zero-field bulk critical temperature…

We introduce a transfer matrix formalism for the (annealed) Ising model coupled to two-dimensional causal dynamical triangulations. Using the Krein-Rutman theory of positivity preserving operators we study several properties of the emerging…

We investigated numerically an Ising model coupled to two-dimensional Euclidean gravity with spherical topology, using Regge calculus with the $dl/l$ path-integral measure to discretize the gravitational interaction. Previous studies of…