Related papers: Stochastic domination for the Ising and fuzzy Pott…
The HEat modulated Infinite DImensional Heston (HEIDIH) model and its numerical approximation are introduced and analyzed. This model falls into the general framework of infinite dimensional Heston stochastic volatility models of (F.E.…
The critical behaviour of the Ising model in the absence of an external magnetic field can be specified either through spontaneous symmetry breaking (thermal criticality) or through cluster percolation (geometric criticality). We extend…
The present paper focuses on the order-disorder transition of an Ising model on a self-similar lattice. We present a detailed numerical study, based on the Monte Carlo method in conjunction with the finite size scaling method, of the…
Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms…
Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a…
We analyze the critical behaviour of the three-dimensional, three-state Potts model in the presence of an external ordering field. From a finite size scaling analysis on lattices of size up to 70**3 we determine the critical endpoint of the…
Phase transitions, as one of the most intriguing phenomena in nature, are divided into first-order phase transitions (FOPTs) and continuous ones in current classification. While the latter shows striking phenomena of scaling and…
A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity…
Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite dimensional) Wiener…
We study an alternative approach to model the dynamical behaviors of biological feedback loop, that is, a type-dependent spin system, this class of stochastic models was introduced by Fern\'andez et. al (2009), and are useful since take…
Machine learning-inspired techniques have emerged as a new paradigm for analysis of phase transitions in quantum matter. In this work, we introduce a supervised learning algorithm for studying critical phenomena from measurement data, which…
The theory of phase transitions is based on the consideration of "idealized" models, such as the Ising model: a system of magnetic moments living on a cubic lattice and having only two accessible states. For simplicity the interaction is…
The dynamical evolution of a recently introduced one dimensional model in \cite{biswas-sen} (henceforth referred to as model I), has been made stochastic by introducing a parameter $\beta$ such that $\beta =0$ corresponds to the Ising model…
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…
Optimal growth of structures governed by spatially stochastic dynamics arises in many scientific settings, for example in processes such as solution-based crystallization and the formation of microbial biofilms on patterned substrates or…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
In this paper, we study the large deviation principle of invariant measures of stochastic reaction-diffusion lattice systems driven by multiplicative noise. We first show that any limit of a sequence of invariant measures of the stochastic…
Ising or Potts models of ferromagnetism have been widely used to describe locally interacting social or economic systems. We consider a related model, introduced by Sznajd to describe the evolution of consensus in a society. In this model,…
We study a non-monotonic behavior of the Binder parameter, which appears in the discrete spin systems. We show that the Binder parameters of the Potts model are non-monotonic for $q=3$ and $4$, while they are monotonic for the Ising case…
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…