相关论文: A Modified Ising Model of Barab\'asi-Albert Networ…
We investigate analytically the behavior of Ising model on two connected Barabasi-Albert networks. Depending on relative ordering of both networks there are two possible phases corresponding to parallel or antiparallel alingment of spins in…
Networks that have power-law connectivity, commonly referred to as the scale-free networks, are an important class of complex networks. A heterogeneous mean-field approximation has been previously proposed for the Ising model of the…
In order to investigate the role of the weight in weighted networks, the collective behavior of the Ising system on weighted regular networks is studied by numerical simulation. In our model, the coupling strength between spins is inversely…
Biological information processing networks consist of many components, which are coupled by an even larger number of complex multivariate interactions. However, analyses of data sets from fields as diverse as neuroscience, molecular…
We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures…
We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\"os-R\'enyi random graphs. We derive analytical expressions…
One of the aims of systems biology is to build multiple layered and multiple scale models of living systems which can efficiently describe phenomena occurring at various level of resolution. Such models should consist of layers of various…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
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.…
Nonreciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit and the critical behavior of the…
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…
This chapter provides a general introduction of network modeling in psychometrics. The chapter starts with an introduction to the statistical model formulation of pairwise Markov random fields (PMRF), followed by an introduction of the PMRF…
We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a…
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e.,…
Several recent experiments in biology study systems composed of several interacting elements, for example neuron networks. Normally, measurements describe only the collective behavior of the system, even if in most cases we would like to…
We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under…
We present a neuronal network model inspired by the Ising model, where each neuron is a binary spin ($s_i = \pm1$) interacting with its neighbors on a 2D lattice. Updates are asynchronous and follow Metropolis dynamics, with a…
Systems with nonreciprocal interactions generically display time-dependent states. These are routinely observed in finite systems, from neuroscience to active matter, in which globally ordered oscillations exist. However, the stability of…
On directed Barabasi-Albert networks with two and seven neighbours selected by each added site, the Ising model with spin S=1/2 was seen not to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation…
To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in…