Relaxation transitions in spin systems

L. B. loffe

Kyozi Kawasaki

R. W. Gibberd, G.C. Stey

Yoshihiko Nonomura, Yusuke Tomita

Although the nonequilibrium-relaxation (NER) method has been widely used in Monte Carlo studies on phase transitions in classical spin systems, such studies have been quite limited in quantum phase transitions. The reason is that the relaxation process based on cluster-update quantum Monte Carlo (QMC) algorithms, which are now standards in Monte Carlo studies on quantum systems, has been considered "too fast" for such analyses. Recently, the present authors revealed that the NER process in classical spin systems based on cluster-update algorithms is characterized by stretched-exponential critical relaxation, rather than conventional power-law relaxation in local-update algorithms. In the present article, we show that this is also the case in quantum phase transitions analyzed with the cluster-update QMC. As the simplest example of isotropic quantum spin models that exhibit quantum phase transitions, we investigate the Néel-dimer quantum phase transition in the two-dimensional S=1/2 columnar-dimerized antiferromagnetic Heisenberg model with the continuous-time loop algorithm, and we confirm stretched-exponential critical relaxation consistent with the three-dimensional classical Heisenberg model in the Swendsen-Wang algorithm.

R. H. Terwiel, Paweł O. Mazur

M. V. Feigel’man, L. B. Ioffe

We consider two realistic models of spin glasses : the Edwards-Anderson model with long-range interaction and the system of classical vector spins with RKKY interaction, and show that in the both models non-exponential relaxation occurs far above the transition point and even in the critical region. We obtain the form of the relaxation q(t) = for long times, in these models.