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Large interacting systems in biology often exhibit emergent dynamics, such as coexistence of multiple time scales, manifested by fat tails in the distribution of waiting times. While existing tools in statistical inference, such as maximum…
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…
We carry out simulated annealing and employ a generalized Kibble-Zurek scaling hypothesis to study the 2D Ising spin glass with normal-distributed couplings. The system has an equilibrium glass transition at temperature $T=0$. From a…
We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the…
Spin-dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of the classical Heisenberg antiferromagnet in simple cubic lattices with linear sizes $L\leq 60$. This system is widely recognized as an…
In this article, we review the metastable hierarchy in low-temperature lattice models. In the first part, we state that for any abstract lattice system governed by a Hamiltonian potential and evolving according to a Metropolis-type…
The stability of a discrete time crystal against thermal fluctuations has been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert equation of a periodically-driven classical system composed of interacting spins, each of…
Over the past decades, a fascinating computational phase transition has been identified in sampling from Gibbs distributions. Though, the computational complexity at the critical point remains poorly understood, as previous algorithmic and…
Magnetic susceptibility and muon spin relaxation (muSR) experiments have been carried out on the quasi-2D triangular-lattice spin S = 2 antiferromagnet FeGa2S4. The muSR data indicate a sharp onset of a frozen or nearly-frozen spin state at…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
We show that in suitable anisotropic ferromagnets, both stable and metastable ``tilted'' phases occur, in which the magnetization ${\vec M}$ makes an angle between zero and $180$ degrees with the externally applied ${\vec H}$. Tuning either…
We study the spin-glass transition in several Ising models of relevance for quantum annealers. We extract the spin-glass critical temperature by extrapolating the pseudo-critical properties obtained with Replica-Exchange Monte-Carlo 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.…
After a sudden quench from the disordered high-temperature $T_0\to\infty$ phase to a final temperature below the critical point $T_F \ll T_c$, the non-conserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a…
We present dynamical properties of spin crossover compounds with photomagnetization, proposing a new model in which the spin-crossover phenomena and magnetic ordering are incorporated in a unified way. By using this model, the novel…
In this study, the temperature variations of the equilibrium and the non-equilibrium antiferromagnetic and ferromagnetic susceptibilities of a metamagnetic system are examined near the critical point. The kinetic equations describing the…
We study the metastable behaviour of a stochastic system of particles with hard-core interactions in a high-density regime. Particles sit on the vertices of a bipartite graph. New particles appear subject to a neighbourhood exclusion…
We present a comparative study of the fate of an Ising ferromagnet on the square lattice with periodic boundary conditions evolving under three different zero-temperature dynamics. The first one is Glauber dynamics, the two other dynamics…
We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization,…
An equilibrated model glass-forming liquid is studied by mapping successive configurations produced by molecular dynamics simulation onto a time series of inherent structures (local minima in the potential energy). Using this ``inherent…