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We consider the ordering dynamics of the Ising model on a square lattice where an additional fixed number of bonds connect any two sites chosen randomly. The total number of shortcuts added is controlled by two parameters $p$ and $\alpha$.…
We introduce a new microcanonical dynamics for a large class of Ising systems isolated or maintained out of equilibrium by contact with thermostats at different temperatures. Such a dynamics is very general and can be used in a wide range…
The emergence of global order in complex systems with locally interacting components is most striking at criticality, where small changes in control parameters result in a sudden global re-organization. We introduce a measure of…
We study the equilibrium and dynamic phase transition properties of two-dimensional Ising model on a decorated triangular lattice under the influence of a time-dependent magnetic field composed of a periodic square wave part plus a time…
The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree…
We study a cellular automaton opinion formation model of Ising type, with antiferromagnetic pair interactions modeling anticonformism, and ferromagnetic plaquette terms modeling the social norm constraints. For a sufficiently large…
We investigate the stochastic resonance phenomena in the field-driven Ising model on small-world networks. The response of the magnetization to an oscillating magnetic field is examined by means of Monte Carlo dynamic simulations, with the…
A nonequilibrium system of locally interacting elements in a lattice with an absorbing order-disorder phase transition is studied under the effect of additional interacting fields. These fields are shown to produce interesting effects in…
We investigate the robustness of a dynamical phase transition against quantum fluctuations by studying the impact of a ferromagnetic nearest-neighbour spin interaction in one spatial dimension on the non-equilibrium dynamical phase diagram…
We study the non-equilibrium phase diagram of a fully-connected Ising $p$-spin model, for generic $p>2$, and investigate its robustness with respect to the inclusion of spin-wave fluctuations, resulting from a ferromagnetic, short-range…
We examine the ordering behavior of the ferromagnetic Ising lattice model defined on a surface with a constant negative curvature. Small-sized ferromagnetic domains are observed to exist at temperatures far greater than the critical…
In this work, we have studied the Ising model with one- and two-spin flip competing dynamics on a two-dimensional additive small-world network (A-SWN). The system model consists of a $L\times L$ square lattice where each site of the lattice…
Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies…
We study the Ising model in a hierarchical small-world network by renormalization group analysis, and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges.…
We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of four-fold coordinated sites connected via variable length one-dimensional chains.…
We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the…
Tipping elements in the Earth System receive increased scientific attention over the recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element…
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…
Non-dyadic higher-order interactions affect collective behavior in various networked dynamical systems. Here we discuss the properties of a novel Ising model with higher-order interactions and characterize its phase transitions between the…
We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified…