相关论文: Strong Spatial Mixing and Approximating Partition …

We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under…

We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice ${\mathbb Z}^d$. This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is…

In the presented article we present an algorithm for the computation of ground state spin configurations for the 2d random bond Ising model on planar triangular lattice graphs. Therefore, it is explained how the respective ground state…

We consider the most general single-spin-flip dynamics for the ferromagnetic Ising chain with nearest-neighbour influence and spin reversal symmetry. This dynamics is a two-parameter extension of Glauber dynamics corresponding respectively…

We analyze the ferromagnetic Ising model on a scale-free tree; the growing random network model with the linear attachment kernel $A_k=k+\alpha$ introduced by [Krapivsky et al.: Phys. Rev. Lett. {\bf 85} (2000) 4629-4632]. We derive an…

We investigate perfect matchings and essential spanning forests in planar hyperbolic graphs via circle packings. We prove the existence of nonconstant harmonic Dirichlet functions that vanish in a closed set of the boundary, generalizing a…

We compute the finite-temperature phase diagram of a pseudospin-$1/2$ Bose gas with contact interactions, using two complementary methods: the random phase approximation (RPA) and self-consistent Hartree-Fock theory. We show that the…

There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via functional inequalities such as Poincar\'e inequalities. In many situations, Markov chains fail to mix rapidly from a worst-case initialization, yet…

We present local mappings that relate the marginal probabilities of a global probability mass function represented by its primal normal factor graph to the corresponding marginal probabilities in its dual normal factor graph. The mapping is…

Motivated by recent spin- and angular-resolved photoemission (SARPES) measurements performed on the two-dimensional electronic states confined near the (001) surface of SrTiO$_3$ in the presence of oxygen vacancies, we explore their spin…

We present a numerical study based on Monte Carlo algorithm of the magnetic properties of a mixed Ising ferrimagnetic model on a cubic lattice where spins $\sigma =\pm 1/2$ and spins $S=0,\pm 1$ are in alternating sites on the lattice. We…

True ground states are evaluated for a 2d Ising model with random near neighbor interactions and ferromagnetic second neighbor interactions (the Randomly Coupled Ferromagnet). The spin glass stiffness exponent is positive when the absolute…

We consider the Edwards-Anderson Ising spin glass model on the half-plane $Z \times Z^+$ with zero external field and a wide range of choices, including mean zero Gaussian, for the common distribution of the collection J of i.i.d. nearest…

Non-equilibrium dynamics of classical random Ising spin chains are studied using asymptotically exact real space renormalization group. Specifically the random field Ising model with and without an applied field (and the Ising spin glass…

There is proposed a model of scale-free random graphs which are locally close to the uncorrelated complex random networks with divergent $\langle k^2 \rangle$ studied in e.g. S. N. Dorogovtsev {\it et al}, Rev. Mod. Phys. {\bf 80}, 1275…

The theory of spin drift and diffusion in two-dimensional electron gases is developed in terms of a random walk model incorporating Rashba, linear and cubic Dresselhaus, and intersubband spin-orbit couplings. The additional subband degree…

Typically two particles (spins) could be maximally entangled at zero temperature, and for a certain temperature the phenomenon of entanglement vanishes at the threshold temperature. For the Heisenberg coupled model or even the Ising model…

The s=3/2 Ising spin chain with uniform nearest-neighbor coupling, quadratic single-site potential, and magnetic field is shown to be equivalent to a system of 17 species of particles with internal structure. The same set of particles (with…

In this work we show that for every $d < \infty$ and the Ising model defined on $G(n,d/n)$, there exists a $\beta_d > 0$, such that for all $\beta < \beta_d$ with probability going to 1 as $n \to \infty$, the mixing time of the dynamics on…

Using exact diagonalization, Monte-Carlo, and mean-field techniques, characteristic temperature scales for ferromagnetic order are discussed for the Ising and the classical anisotropic Heisenberg model on finite lattices in one and two…