Universality and Dynamical Behaviour in Pure and Disordered Spin-1 Models

Martin Hasenbusch B, Andrea Pelissetto C, Ettore Vicari

We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the ± J Ising model along the paramagnetic–ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size dependence of suitably defined autocorrelation times at the critical point provides the estimate z = 2.35(2) for the universal dynamic critical exponent. We also study the off-equilibrium relaxational dynamics following a quench from to T c . In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behaviour gives an estimate of z that is perfectly consistent with the equilibrium estimate z = 2.35(2).

Erhard Seiler, Ion Olimpiu Stamatescu, Adrian Patrascioiu +1 more

Sascha Wald, Malte Henkel, Andrea Gambassi

Abstract The collective and purely relaxational dynamics of quantum many-body systems after a quench at temperature T = 0, from a disordered state to various phases is studied through the exact solution of the quantum Langevin equation of the spherical and the O ( n )-model in the limit n → ∞. The stationary state of the quantum dynamics is shown to be a non-equilibrium state. The quantum spherical and the quantum O ( n )-model for n → ∞ are in the same dynamical universality class. The long-time behaviour of single-time and two-time correlation and response functions is analysed and the universal exponents which characterise quantum coarsening and quantum ageing are derived. The importance of the non-Markovian long-time memory of the quantum noise is elucidated by comparing it with an effective Markovian noise having the same scaling behaviour and with the case of non-equilibrium classical dynamics.

Joaquin F. Rodriguez-Nieva, Saraswat Bhattacharyya, Dries Sels +1 more

Raoul Santachiara

It is known that the entropy of a block of spins of size L embedded in an infinite pure critical spin chain diverges as the logarithm of L with a prefactor fixed by the central charge of the correspondent conformal field theory. For a class of strongly random spin chains, it has been shown that the correspondent block entropy still remains universal and diverges logarithmically with an ‘effective’ central charge. By computing the entanglement entropy for a family of models which includes the N -states random Potts chain and the Z N clock model, we give some definitive answer to recent conjectures about the behaviour of this effective central charge. In particular, we show that the ratio between the entanglement entropy in the pure and in the disordered system is model dependent and we provide a series of critical models where the entanglement entropy grows from the pure to the random case.

Rajiv R. P. Singh, Martin P. Gelfand