Related papers: Nature vs. Nurture in Discrete Spin Dynamics
The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…
Niching enables a genetic algorithm (GA) to maintain diversity in a population. It is particularly useful when the problem has multiple optima where the aim is to find all or as many as possible of these optima. When the fitness landscape…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
We study the processes in which fluctuating elements of a system are progressively fixed (quenched) while keeping the interaction with the remaining unfixed elements. If the interaction is global among the Ising spin elements and if the…
We consider N initially disentangled spins, embedded in a ring or d-dimensional lattice of arbitrary geometry, which interact via some long--range Ising--type interaction. We investigate relations between entanglement properties of the…
The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the…
In this paper we define a variant of the Ising model in which spins are replaced with permutations. The energy between two spins is a function of the relative disorder of one spin, a permutation, to the other. This model is motivated by a…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
We investigate the classical nature of the spin coherent states. In addition to being minimum uncertainty states, as the size of the spin, S, increases, the classical nature is seen to increase in two respects: in their resistance to…
Discrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied, for the number of states $q=3,4$ in $d$…
The mixed spin-(1/2, 1) Ising model on two fully frustrated triangles-in-triangles lattices is exactly solved with the help of the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the…
In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multi-stable systems, many attractors coexist so that their basins of attraction…
In quenched disordered systems, the existence of ordering is generally believed to be only possible in the weak disorder regime (disregarding models of spin-glass type). In particular, sufficiently large random fields is expected to…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
The zero-field isothermal susceptibility of the one-dimensional Ising model with nearest-neighbor interactions and a finite number of spins is shown to have a relatively simple singularity as the temperature approaches zero, proportional…
We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system…
Animals' internal states reflect variables like their position in space, orientation, decisions, and motor actions -- but how should these internal states be arranged? Internal states which frequently transition between one another should…
We study systems with a continuous phase transition that tune their parameters to maximize a quantity that diverges solely at a unique critical point. Varying the size of these systems with dynamically adjusting parameters, the same…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
Computation plays a key role in predicting and analyzing natural phenomena. There are two fundamental barriers to our ability to computationally understand the long-term behavior of a dynamical system that describes a natural process. The…