Related papers: Dynamical Replica Theory for Disordered Spin Syste…
The problem of spin diffusion is studied numerically in one-dimensional classical Heisenberg model using a deterministic odd even spin precession dynamics. We demonstrate that spin diffusion in this model, like energy diffusion, is normal…
A growing body of theoretical and empirical evidence shows that the global steady-state distributions of many equilibrium and nonequilibrium systems approximately satisfy an analogue of the Boltzmann distribution, with a local dynamical…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
A review of the replica symmetric solution of the classical and quantum, infinite-range, Sherrington-Kirkpatrick spin glass is presented.
We investigate near the point of glass transition the expansion of the free energy corresponding to the generalized Sherrington--Kirkpatrick model with arbitrary diagonal operators U standing instead of Ising spins. We focus on the case…
In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise…
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…
Glassy soft matter is often continuously polydisperse, in which the sizes or various properties of the constituent particles are distributed continuously. However, most of the microscopic theories of the glass transition focus on the…
The interpolation method for mean field spin glass models developed by Guerra and Talagrand is extended to a quantum mean field spin glass model. This extension enables us to obtain both replica-symmetric (RS) and one step replica-symmetry…
We present a new dynamical proof of the Thouless-Anderson-Palmer (TAP) equations for the classical Sherrington-Kirkpatrick spin glass at sufficiently high temperature. In our derivation, the TAP equations are a simple consequence of the…
Sinai's model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields asymptotically exact long time results. The distribution of the position of a particle and the probability of…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reaction-diffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two…
We calculate the probability distribution of the overlap between a spin glass and a copy of itself in which the bonds are randomly perturbed in varying degrees. The overlap distribution is shown to go to a delta distribution in the…
We study the problem of spin diffusion in magnetic systems without long-range order. We discuss the example of the 1D spin chain. For the system described by the Heisenberg Hamiltonian we show that there are no diffusive excitations.…
We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the…
We investigate an XY spin-glass model in which both spins and couplings evolve in time: the spins change rapidly according to Glauber-type rules, whereas the couplings evolve slowly with a dynamics involving spin correlations and Gaussian…
This paper is devoted to the analysis of some fundamental problems of linear elasticity in 1D continua with self-similar interparticle interactions. We introduce a self-similar continuous field approach where the self-similarity is…
The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. The averaged physical quantities are to be represented via…