Related papers: Partition function for several Ising model interfa…
Ising machines, which are dynamical systems designed to operate in a parallel and iterative manner, have emerged as a new paradigm for solving combinatorial optimization problems. Despite computational advantages, the quality of solutions…
In order to gain a better understanding of the Ising model in higher dimensions we have made a comparative study of how the boundary, open versus cyclic, of a d-dimensional simple lattice, for d=1,...,5, affects the behaviour of the…
We review a class of energy landscape analysis method that uses the Ising model and takes multivariate time series data as input. The method allows one to capture dynamics of the data as trajectories of a ball from one basin to a different…
We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a…
The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We will obtain the potential scattering amplitude form the complete Green function in the corresponding…
The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations…
Spatial correlations - bubbles, domain walls, etc. - can best be studied by concentrating on the degrees of freedom most relevant to the problem. For the finite temperature confinement transition, I integrate out all gauge degrees of…
In order to gain a deeper understanding of complex systems and infer key information using minimal data, I classify all configurations based on classical probability, starting from the dimensions of energy and different categories of…
A recently developed technique for the determination of the density of partition function zeroes using data coming from finite-size systems is extended to deal with cases where the zeroes are not restricted to a curve in the complex plane…
We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
Steady-state solutions of the Poisson-Nernst-Planck model are studied in the asymptotic limit of large, but finite domains. By using asymptotic matching for integrals, we derive an approximate solution for the steady-state equation with…
The stacking problem is approached by computational mechanics, using an Ising next nearest neighbor model. Computational mechanics allows to treat the stacking arrangement as an information processing system in the light of a symbol…
This work establishes links between the Ising model and elliptic curves via Mahler measures. First, we reformulate the partition function of the Ising model on the square, triangular and honeycomb lattices in terms of the Mahler measure of…
We adapt the semiclassical technique, as used in the context of instanton transitions in quantum field theory, to the description of tunneling transmissions at finite energies through potential barriers by complex quantum mechanical…
Systems with many interacting stochastic constituents are fully characterized by their free energy. Computing this quantity is therefore the objective of various approaches, notably perturbative expansions, which are applied in problems…
By quenching into the metastable region of the three-dimensional Ising model, we investigate the paths that the magnetization (energy) takes as a function of time. We accumulate the magnetization (energy) paths into time-dependent…
Two improvements with respect to previous formulations are presented for the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems. By including anharmonicities and employing a variational…
Free-discontinuity problems describe situations where the solution of interest is defined by a function and a lower dimensional set consisting of the discontinuities of the function. Hence, the derivative of the solution is assumed to be a…
In this paper a new approach to solving the Ising-Onsager problem in external magnetic field is investigated. The expression for free energy on one Ising spin in external field both for the twodimensional and threedimensional Ising model…