Related papers: Decay of the metastable phase in d=1 and d=2 Ising…
We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase…
It is widely accepted that the free energy F(H) of the two-dimensional Ising model in the ferromagnetic phase T<T_c has an essential branch cut singularity at the origin H=0. The phenomenological droplet theory predicts that near the cut…
We review some aspects of current knowledge regarding the decay of metastable phases in many-particle systems. In particular we emphasize recent theoretical and computational developments and numerical results regarding homogeneous…
This work extends to dimension $d\geq3$ the main result of Dehghanpour and Schonmann. We consider the stochastic Ising model on ${\mathbb{Z}}^d$ evolving with the Metropolis dynamics under a fixed small positive magnetic field $h$ starting…
Open driven quantum systems have defined a powerful paradigm of nonequilibrium phases and phase transitions; however, quantum phase transitions are generically not expected in this setting due to the decohering effect of dissipation. In…
We study the two-dimensional kinetic Ising model below its equilibrium critical temperature, subject to a square-wave oscillating external field. We focus on the multi-droplet regime where the metastable phase decays through nucleation and…
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…
We investigate the dynamical critical behavior of the two- and three-dimensional Ising model with Glauber dynamics in equilibrium. In contrast to the usual standing, we focus on the mean-squared deviation of the magnetization $M$, MSD$_M$,…
The dynamics of a random (quenched) field Ising model (in two dimension) at zero temperature in the presence of an additional sinusoidally oscillating homogeneous (in space) magnetic field has been studied by Monte Carlo simulation using…
We investigate the dissipative loss in the $\pm J$ Ising spin glass in three dimensions through the scaling of the hysteresis area, for a maximum magnetic field that is equal to the saturation field. We perform a systematic analysis for the…
The spontaneous magnetization is proved to vanish continuously at the critical temperature for a class of ferromagnetic Ising spin systems which includes the nearest neighbor ferromagnetic Ising spin model on $\mathbb Z^d$ in $d=3$…
By quenching into the metastable region of the three-dimensional Ising model, we investigate the paths that the magnetization (energy) takes as a function of time. We accumulate the magnetization (energy) paths into time-dependent…
We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy…
We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent $\gamma$. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for…
Applying a numerical transfer-matrix formalism, we obtain complex-valued constrained free energies for the two-dimensional square-lattice nearest-neighbor Ising ferromagnet below its critical temperature and in an external magnetic field.…
The mechanism of appearance of exponentially large number of metastable states in magnetic phases of disordered Ising magnets with short-range random exchange is suggested. It is based on the assumption that transitions into inhomogeneous…
We study the correlation function of the one-dimensional Ising model at fixed magnetization. Focusing on the scaling limit close to the zero-temperature fixed point, we show that this correlation function, in momentum space, exhibits…
In the present chapter, we focus on the switching of magnetisation, or the metastable lifetime of a ferromagnetic system. In this regard, particularly the Ising model and the Blume-Capel model, have been simulated in the presence of an…
The far-from-equilibrium low-temperature dynamics of ultra-thin magnetic films is analyzed by using Monte Carlo numerical simulations on a two dimensional Ising model with competing exchange ($J_0$) and dipolar ($J_d$) interactions. In…
We apply both a scalar field theory and a recently developed transfer-matrix method to study the stationary properties of metastability in a two-state model with weak, long-range interactions: the $N$$\times$$\infty$ quasi-one-dimensional…