Nature of the "Griffiths" Singularity in Dilute Magnets
نویسنده
چکیده
The nature of the singular behavior pointed out by Griffiths for H=0 in dilute magnets is investigated. It is argued that for concentration p less than that for formation of an infinite cluster, all derivatives of M(H) are finite. The nonanalyticity in M(H) is due to a branch cut along the imaginary H axis having weight exp[−(const)/|H|] for |H|→0, and is thus too weak to be experimentally observable. Some numerical and exact analytic results for the dilute magnet on a Bethe lattice are presented.
منابع مشابه
Griffiths Singularities in the Dynamics of Disordered Ising
We study the asymptotic behaviour of the correlation function q(t)= l N =-(Si(0) Si@>) for dilute, short-range Ising ferromagnets and spin glasses with single spin-N i-1 flip dynamics, Using an eigenfunction expansion for the time evolution operator and a variational estimate for the gap in the spectrum of this operator, we prove that, for a range of temperatures above the T, of the random syst...
متن کاملRelaxation of Disordered Magnets in the Griffiths’ Regime
We study the relaxation to equilibrium of discrete spin systems with random finite range (not necessarily ferromagnetic) interactions in the Griffiths’ regime. We prove that the speed of convergence to the unique reversible Gibbs measure is almost surely faster than any stretched exponential, at least if the probability distribution of the interaction decays faster than exponential (e.g. Gaussi...
متن کاملA Monte Carlo algorithm for sampling rare events: application to a search for the Griffiths singularity
We develop a recently proposed importance-sampling Monte Carlo algorithm for sampling rare events and quenched variables in random disordered systems. We apply it to a two dimensional bond-diluted Ising model and study the Griffiths singularity which is considered to be due to the existence of rare large clusters. It is found that the distribution of the inverse susceptibility has an exponentia...
متن کاملRelaxation to Equilibrium for Two Dimensional Disordered Ising Systems in the Griffiths Phase
We consider Glauber–type dynamics for two dimensional disordered magnets of Ising type. We prove that, if the disorder–averaged influence of the boundary condition is sufficiently small in the equilibrium system, then the corresponding Glauber dynamics is ergodic with probability one and the disorder–average C(t) of time–autocorrelation function satisfies C(t) . e−m(log t) (for large t). For th...
متن کاملRandom Quantum Magnets with Long-Range Correlated Disorder: Enhancement of Critical and Griffiths-McCoy Singularities
We study the effect of spatial correlations on quenched disorder in random quantum magnets at and near a quantum critical point. In random transverse-field Ising systems disorder correlations that decay algebraically with an exponent r change the universality class of the transition for small enough r, and off-critical Griffiths-McCoy singularities are enhanced. We present exact results for 1D ...
متن کامل