Related papers: Phase Transition for Glauber Dynamics for Independ…
We revisit the Glauber model to study the heavy ion reaction cross sections and elastic scattering angular distributions at low and intermediate energies. The Glauber model takes nucleon-nucleon cross sections and nuclear densities as…
Cell monolayers and epithelial tissues display slow dynamics during the liquid-glass transitions, a phenomenon with direct relevance to embryogenesis, tumor metastases, and wound healing. In active cells, persistent motion and cell…
The Swendsen-Wang dynamics is a popular algorithm for sampling from the Gibbs distribution for the ferromagnetic Ising model on a graph $G=(V,E)$. The dynamics is a "global" Markov chain which is conjectured to converge to equilibrium in…
We consider the soft-core Widom-Rowlinson model for particles with spins and holes, on a Cayley tree of order $d$ (which has $d + 1$ nearest neighbours), depending on repulsion strength $\beta$ between particles of different signs and on an…
Recently, we introduced [Physical Review E 100, 022303 (2019)] a stochastic social balance model with Glauber dynamics which takes into account the role of randomness in the individual's behavior. One important finding of our study was a…
This work establishes novel optimum mixing bounds for the Glauber dynamics on the Hard-core and Ising models. These bounds are expressed in terms of the local connective constant of the underlying graph $G$. This is a notion of effective…
We consider a slight modification of the frog model. For a given graph, each vertex has $\mathrm{Poisson}(\lambda)$ particles (or frogs). At time zero, only the particles at the origin are active, and all the other particles are sleeping.…
In this article, we briefly review the studies on magnetic relaxation behaviours. The theoretical as well as experimental investigations are reported briefly. A major part of this article is devoted to the recent Monte Carlo investigations…
The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…
In a recent publication we established an analogy between the free energy of a hard sphere system and the energy of an elastic network [1]. This result enables one to study the free energy landscape of hard spheres, in particular to define…
We have considered the dynamical evolution of cellular patterns controlled by a stochastic Glauber process determined by the deviations of local cell topology from that of a crystalline structure. Above a critical temperature evolution is…
A voting model (or a generalization of the Glauber model at zero temperature) on a multidimensional lattice is defined as a system composed of a lattice each site of which is either empty or occupied by a single particle. The reactions of…
We study the mixing time of Glauber dynamics on monotone systems. For monotone systems satisfying the entropic independence condition, we prove a new mixing time comparison result for Glauber dynamics. For concrete applications, we obtain…
We investigate the metastable behavior of the long-range Ising model on random regular graphs under Glauber dynamics at low-temperature. We estimate the energy barrier and exit time from the metastable state using a nontrivial path-wise…
We illuminate the many-body effects underlying the structure, formation, and dissolution of cellular adhesion domains in the presence and absence of forces. We consider mixed Glauber-Kawasaki dynamics of a two-dimensional model of…
We study the multi-component Ising model, which is also known as the block Ising model. In this model, the particles are partitioned into a fixed number of groups with a fixed proportion, and the interaction strength is determined by the…
Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons…
We present novel results for fast mixing of Glauber dynamics using the newly introduced and powerful Spectral Independence method from [Anari, Liu, Oveis-Gharan: FOCS 2020]. We mainly focus on the Hard-core model and the Ising model. We…
We analyze, within a mean-field approach, the stationary states of the kinetic spin-3/2 Blume-Capel model by the Glauber-type stochastic dynamics and subject to a time-dependent oscillating external magnetic field. The dynamic phase…
We study phase-ordering dynamics of a ferromagnetic system with a scalar order-parameter on fractal graphs. We propose a scaling approach, inspired by renormalization group ideas, where a crossover between distinct dynamical behaviors is…