Related papers: Metastability for Glauber dynamics on the complete…
The wavefunction of a single spin system in a prepared initial state evolves to equilibrium with a heat bath. The average spin $$q(t) = p_{\uparrow}(t) - p_{\downarrow}(t)$$ exhibits a characteristic time for this evolution. With the proper…
We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O($N$)-symmetric universality classes, including the $N\to 0$ limit that describes the critical behavior of…
We consider the Ising model on the hexagonal lattice evolving according to Metropolis dynamics. We study its metastable behavior in the limit of vanishing temperature when the system is immersed in a small external magnetic field. We…
We study the microscopic dynamics of the metastable Quasi-Stationary States (QSS) in the Hamiltonian Mean Field (HMF) model, a Hamiltonian system of N classical inertial spins with infinite-range interactions which shows a second order…
The element of metastability is incorporated in the fluctuating nonlinear hydrodynamic description of the mode coupling theory (MCT) of the liquid-glass transition. This is achieved through the introduction of the defect density variable…
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…
We consider $h$-stable local optima of Ising spin glass models, defined as spin configurations such that for nearly all of the spins, flipping their values results in increasing energy by at least a given amount $h$. Spins satisfying this…
The Kuramoto model with mixed signs of couplings is known to produce a traveling-wave synchronized state. Here, we consider an abrupt synchronization transition from the incoherent state to the traveling-wave state through a long-lasting…
In spin-crossover materials, the volume of a molecule changes depending on whether it is in the high-spin (HS) or low-spin (LS) state. This change causes distortion of the lattice. Elastic interactions among these distortions play an…
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…
Consider Glauber dynamics for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a metastable state with negative magnetization. Slowly the…
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…
Understanding the low-temperature pure state structure of spin glasses remains an open problem in the field of statistical mechanics of disordered systems. Here we study Monte Carlo dynamics, performing simulations of the growth of…
We study the critical behavior and the out-of-equilibrium dynamics of a two-dimensional Ising model with non-static interactions. In our model, bonds are dynamically changing according to a majority rule depending on the set of closest…
Heat bath Monte Carlo simulations have been used to study a 12-state discretized Heisenberg model with a type of random field, for several values of the randomness coupling parameter $h_R$. The 12 states correspond to the [110] directions…
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…
We investigate the nematic phase transition in the Heisenberg $J_1$-$J_2$-model on square and triangular lattices, accounting for finite lattice compressibility and bond-length-dependent magnetic exchange. Using Nematic Bond Theory, a…
We prove an optimal $\Omega(n^{-1})$ lower bound on the spectral gap of Glauber dynamics for anti-ferromagnetic two-spin systems with $n$ vertices in the tree uniqueness regime. This spectral gap holds for all, including unbounded, maximum…
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 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…