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A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
A novel order parameter $\Phi$ for spin glasses is defined based on topological criteria and with a clear physical interpretation. $\Phi$ is first investigated for well known magnetic systems and then applied to the Edwards-Anderson $\pm J$…
Using Suzuki-Trotter decompositions of exponential operators we describe new algorithms for the numerical integration of the equations of motion for classical spin systems. These techniques conserve spin length exactly and, in special…
A general condition determining the optimal performance of a complex system has not yet been found and the possibility of its existence is unknown. To contribute in this direction, an optimization algorithm as a complex system is presented.…
A spin-1/2 chain model that includes three spin interactions can effectively describe the dynamics of two species of bosons trapped in an optical lattice with a triangular-ladder configuration. A perturbative theoretical approach and…
Correlation measure of order $k$ is an important measure of randomness in binary sequences. This measure tries to look for dependence between several shifted version of a sequence. We study the relation between the correlation measure of…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
Spin-dependent partial conductances are evaluated in a tight-binding description of electron transport in the presence of spin-orbit (SO) couplings, using transfer-matrix methods. As the magnitude of SO interactions increases, the…
The analysis of correlation function data obtained by Monte Carlo simulations of the two-dimensional 4-state Potts model, XY model, and self-dual disordered Ising model at criticality are presented. We study the logarithmic corrections to…
We consider the pair correlation functions of both the order parameter field and its square for phase ordering in the $O(n)$ model with nonconserved order parameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$. We…
Modular robots have the potential to revolutionize automation, as one can optimize their composition for any given task. However, finding optimal compositions is non-trivial. In addition, different compositions require different base…
First-order iterative optimization methods play a fundamental role in large scale optimization and machine learning. This paper presents control interpretations for such optimization methods. First, we give loop-shaping interpretations for…
Determining the phase diagram of systems consisting of smaller subsystems 'connected' via a tunable coupling is a challenging task relevant for a variety of physical settings. A general question is whether new phases, not present in the…
A classical Monte Carlo algorithm based on the quasi-classical approximation is applied to the pseudospin Hamiltonian of the model cuprate. The model takes into account both local and non-local correlations, Heisenberg spin-exchange…
Taking the two-dimensional Ising model for example, short-time behavior of critical dynamics with a conserved order parameter is investigated by Monte Carlo simulations. Scaling behavior is observed, but the dynamic exponent $z$ is updating…
In this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use…
We study the ordering of the spin and the chirality in the fully frustrated XY model on a square lattice by extensive Monte Carlo simulations. Our results indicate unambiguously that the spin and the chirality exhibit separate phase…
We present a method to probe the Out-of-Time-Order Correlators (OTOCs) of a general system by coupling it to a harmonic oscillator probe. When the system's degrees of freedom are traced out, the OTOCs imprint themselves on the generalized…
We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the…
The two-dimensional spin-1 Baxter-Wu model is studied by using Monte Carlo simulations. The standard single-spin-flip Metropolis algorithm is used to generate the configurations from which the order parameter, specific heat and magnetic…