The Shore–Sethna model is one of the simplest spin models including frustration at microscopic level. It consists of a three-dimensional system of Ising spins with ferromagnetic nearest-neighbors and antiferromagnetic next-nearest-neighbors interactions, and the competition between these two...

We consider the effects of a quench to T=0 on a spin system with axial next–next nearest neighbour Ising interactions, evolving under a conserved 3-spin flip dynamics. Such a model is motivated by the kinetics of stacking layers in polytypes near the 3C–6H transition. We find that the system...

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T, a quantum parameter g, and the ratio p=−J2/J1, where J10 refers to ferromagnetic interactions between first-neighbour sites along the d directions of a hypercubic lattice, and J2<0 is associated with competing antiferromagnetic interactions between second neighbours along m≤d directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0 space, with a Lifshitz point at p=1/4, for d>2, and closed-form...</0>

The nature of the dynamics of opinion formation or zero-temperature Ising models modeled as a decision-by-majority process in complex networks is investigated using eigenmode analysis. The Hamiltonian of the system is defined and estimated by eigenvectors of the adjacency matrix constructed from...

The method based on the use of the generating functions of spin correlators was proposed for the description of the Glauber dynamics of disordered Ising chain. The partial differential equations was derived for these generating functions and the formal solutions were obtained. The exact...

Damage spreading(DS) of the random graph networks with power-law degree distributions is investigated using Glauber dynamics. Various subgraphs defined by the probability of acquaintance show distinct features in DS as measured by Hamming distance. A heuristic understanding of the long-time...

We consider Glauber dynamics at zero temperature for the ferromagnetic Ising model on the usual random graph model on N vertices, with on average γ edges incident to each vertex, in the limit as N→∞. Based on numerical simulations, Svenson (Phys. Rev. E 64 (2001) 036122) reported that the...

We study the time-dependent structure factor of the one-dimensional Glauber model upon instantaneous cooling. Results obtained earlier by Reiss, Mazenko and Widom, and Bray, are linked together. Next, finite-size scaling in the limit of zero temperature, long times, small wave vectors, and large...

The time-evolution of the damage in the Ising model with the heat bath and Glauber dynamics has been investigated with the damage spreading method. The damage density D(t) and the average distance r(t) of damaged sites from the origin have been measured numerically. From the simulational data,...