Related papers: Exact matrix model for generalized Ising model
We analyze the collective spin noise in interacting spin systems. General expressions are derived for the short time behaviour of spin systems with general spin-spin interactions, and we suggest optimum experimental conditions for the…
The study of frustrated spin systems often requires time-consuming numerical simulations. As the simplest approach, the classical Ising model is often used to investigate the thermodynamic behavior of such systems. Exploiting the small…
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…
Computation with the Ising model is central to future computing technologies like quantum annealing, adiabatic quantum computing, and thermodynamic classical computing. Traditionally, computed values have been equated with ground states.…
Presented here is an algorithm for a type-II quantum computer which simulates the Ising model in one and two dimensions. It is equivalent to the Metropolis Monte-Carlo method and takes advantage of quantum superposition for random number…
In this study, we present a novel analytical approach to solving large-scale Ising problems by reformulating the discrete Ising Hamiltonian into a continuous framework. This transformation enables us to derive exact solutions for a…
We present a generic framework for describing interacting, spinning, active polar particles, aimed at modelling dense cell aggregates, where cells are treated as polar, rotating objects that interact mechanically with one another and their…
Ordered polarity alignment of a cell population plays a vital role in biology, such as in hair follicle alignment and asymmetric cell division. Here, we propose a theoretical framework for the understanding of generic dynamical properties…
We study the spin-$1/2$ Ising chain with multispin interactions $K$ involving the product of $m$ successive spins, for general values of $m$. Using a change of spin variables the zero-field partition function of a finite chain is obtained…
The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. Fast, compact oscillator networks which provide…
Using an iteration technique, we obtain exact expressions for the free energy and the magnetization of an Ising model on a two - layer Bethe lattice with intralayer coupling constants J1 and J2 for the first and the second layer,…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
The Ising model is studied on a series of hyperbolic two-dimensional lattices which are formed by tessellation of triangles on negatively curved surfaces. In order to treat the hyperbolic lattices, we propose a generalization of the corner…
Ising machines as hardware solvers of combinatorial optimization problems (COPs) can efficiently explore large solution spaces due to their inherent parallelism and physics-based dynamics. Many important COP classes such as satisfiability…
Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes.…
Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to…
Complex systems' modeling and simulation are powerful ways to investigate a multitude of natural phenomena providing extended knowledge on their structure and behavior. However, enhanced modeling and simulation require integration of…
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…
Three-dimensional Ising model in zero external field is exactly solved by operator algebras, similar to the Onsager's approach in two dimensions. The partition function of the simple cubic crystal imposed by the periodic boundary condition…
Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks…