Ising Ring Research Articles

Multipartite nonlocality in a thermalized Ising spin chain

We study multipartite correlations and non-locality in an isotropic Ising ring under transverse magnetic field at both zero and finite temperature. We highlight parity-induced differences between the multipartite Bell-like functions used in order to quantify the degree of non-locality within a ring state and reveal a mechanism for the passive protection of multipartite quantum correlations against thermal spoiling effects that is clearly related to the macroscopic properties of the ring model.

Magnetization dynamics in isolated Ising chains

The Glauber dynamics of an Ising chain or ring is shown to be determined by two characteristic times: τ1 for relaxation of the average magnetization per spin and τ2 for dynamical spontaneous symmetry breaking. An analytical solution for magnetization dynamics in a finite chain with fixed spins at both ends is found by the method of images. This solution is then used to calculate the spin-spin correlation functions for rings and chains. At low temperatures, since τ1 ≫ τ2, there must exist a range of times when the chain is in one of two ordered states.

Wavelet analysis of Ising model spin dynamics

The Burt–Adelson wavelet decomposition was used to analyze the Monte Carlo spin dynamics of a one‐dimensional Ising ring. Burt–Adelson wavelets were used because they select for spin domains and domain walls. For wavelet amplitudes cni(t), we computed mean‐square fluctuations 〈[cni(t)]2〉, spatial correlation functions 〈cni(t)cni+a(t)〉, and time correlation functions 〈cni(t)cni(t+τ)〉. The simulations are in excellent agreement with analytic calculations. The temperature and decomposition order dependencies of the static correlation functions are readily explained by the wavelet support L and the system’s correlation length ξ. High‐order (long‐wavelength) wavelet time correlation functions decay exponentially. Low‐order wavelet time correlation functions have an approximate two‐exponential decay, with a fast temperature‐independent relaxation corresponding to the random walk of domain edges and a slow, temperature‐dependent relaxation corresponding to domain creation and annihilation. At intermediate temperatures the slow decay rate satisfies the scaling relationship Γ−1∼〈[cn(t)]2〉z for z=1.80. © 1995 American Institute of Physics.