Related papers: Completeness of classical spin models and universa…
We review the applications of the integral over anticommuting Grassmann variables (nonquantum fermionic fields) to the analytic solutions and the field-theoretical formulations for the 2D Ising models. The 2D Ising model partition function…
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2d quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We…
We review some aspects of the fermionic interpretation of the two-dimensional Ising model. The use is made of the notion of the integral over the anticommuting Grassmann variables. For simple and more complicated 2D Ising lattices, the…
A general numerical method is presented to locate the partition function zeros in the complex beta plane for large lattice sizes. We apply this method to the 2D Ising model and results are reported for square lattice sizes up tp L=64. We…
We represent a general procedure for calculating the partition function of an Ising model on a one dimensional Fibonacci lattice in presence of magnetic field.This partition function can be written as a sum of partition functions of usual…
While the Ising model remains essential to understand physical phenomena, its natural connection to combinatorial reasoning makes it also one of the best models to probe complex systems in science and engineering. We bring a computational…
We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2--D classical spin systems and 1--D quantum spin systems. The method is scalable and has a controlled error. We illustrate…
The paper discusses the transformation of decorated Ising models into an effective \textit{undecorated} spin models, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The…
We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model…
We propose the mapping of polynomial of degree 2S constructed as a linear combination of powers of spin-$S$ (for simplicity, we called as spin-$S$ polynomial) onto spin-crossover state. The spin-$S$ polynomial in general can be projected…
We derive an exact path integral formulation for the partition function for the Ising model using a mapping between spins and poles of a Laurent expansion for a field on the complex plane. The advantage in using this formulation for the…
Spin models are widely studied in the natural sciences, from investigating magnetic materials in condensed matter physics to studying neural networks. Previous work has demonstrated that there exist simple classical spin models that are…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
We propose a novel way of investigating the universal properties of spin systems by coupling them to an ensemble of causal dynamically triangulated lattices, instead of studying them on a fixed regular or random lattice. Somewhat…
We present a simple construction that maps quantum circuits to graphs and vice-versa. Inspired by the results of D.A. Lidar linking the Ising partition function with quadratically signed weight enumerators (QWGTs), we also present a…
A characteristic feature of the 3d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly…
We propose a method for generalizing the Ising model in magnetic fields and calculating the partition function (exact solution) for the Ising model of an arbitrary shape. Specifically, the partition function is calculated using matrices…
The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel…
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…
The exact solution of the Ising model on the complete graph (CG) provides an important, though mean-field, insight for the theory of continuous phase transitions. Besides the original spin, the Ising model can be formulated in the…